Italy at the time was at its least confusing, perhaps. Genoa was clearly an enemy, the Pope, the Aragonese and the Venetians had united the rest of Italy against it. However, some uncertainty yet remained in northern Italy, where Milan and Savoy, token support aside, still avoided a firm commitment. Things were further complicated there soon after the Turkish invasion, so before we could get to that, some mention is needed of the career of the Duke-Dauphin Louis II (OOC: in OTL - King Louis XI of France). A cunning, ambitious man, he could have become a great French king had dice fallen differently at Agincourt. As it was, in theory at least he had to be content with the Duchy of Dauphine. But that he was not content with - he had ambitions, though not ones aimed at the reconquest of France. After the death of de la Tremoille in 1449, Louis begun taking power into his hands; utilizing the assets at hand, he salvaged and rebuilt his army, replenished the treasury and, in 1457, made his first step with the assassination of Rene, Count of Provence, which then reverted to his reign. In 1460, as the Duke-Dauphin smelt an opportunity, he readied his assets (meaning the soldiers, the mercenaries, the diplomats and the assassins), and struck out. Francesco Sforza, the Duke of Milan whose reign was of a questionable legitimacy (he came to power after a coup d'etat in the conditions of republican chaos), died suddenly - either of old age, either of poison, and soon enough the North Italian duchy descended into the chaos of the Second Ambrosian Republic. Angevin claims that the Duke-Dauphin had towards Milan were immediately renewed, and support amongst some of the local elite was procured. Mercenaries soon captured Milan itself with the help of the aforementioned elite. Fearful, Ludovico of Savoy tried to prevent the creation of a Valois superstate in northern Italy and declared war; he was captured in the battle at Cuneo, and... forced to abdicate in the favour of Louis II. This somewhat rash move, even without the ensuing invasion and conquest of Milan, would have brought all the Mediterranean power against Louis, but for their life-and-death struggle with the Ottoman Empire.
In 1461, while Matthias Corvinus, the brother of King Laszlo II and a brilliant commander, led a campaign that succesfully retook the Serbian capital of Smederevo and caused a recidive of Albanian uprisings (though, disorganized and badly-led as they were, the Albanians were easily defeated), the Italian campaign of Mehmed II had begun. A good half of the Ottoman fleet infiltrated the Adriatic Sea and launched a suicide attack towards Venice that, through its daring, actually reached the city and was only stopped there after a very fierce battle. The Venetians thusly distracted were unable to intercept Mehmed II with the other half of the Ottoman fleet that, having defeated an Aragonese flotilla, has disembarked the finest of the Ottoman army at Otranto. The small garrison there was overwhelmed quickly, and, having left a small garrison, the Ottomans marched out, crossing the Appenines before anyone could react and taking Naples. Despite the rising attrition and the logistical problems that by then begun to come up, the Ottomans had soon set out for Rome. In early 1462, having defeated the Papal-Aragonese armies at Campoleone, Mehmed II has besieged Rome.
Meanwhile, back in North Italy, Genoa's end was clearly coming. The Aragonese were besieging the city, and the Ligurian countryside was held either by them, either by the Duke-Dauphin. Overseas Genoese assets were either in Venetian hands, either (that went, mostly, for their Black Sea colonies) under de facto Turkish control, local specialists indeed agreeing to serve as advisors for the Ottomans, particularily assisting in the construction of the fleet. The Genoese leaders, having no illusions about their future, decided to die proudly along with their city. However, popular pressure was increasing as the situation was getting worse. Finally, the noble family of the Dorias launched a desperate diplomatic gamble. They agreed to give up Genoa without a battle, if they were to become dynastic rulers of the city, ofcourse recognizing the supreme authority of... Louis II, who, knowing all too well that as soon as the Turks and the Genoese were dealt with it would be his turn, has agreed and entered the war on the Turkish-Genoese side, relieving Genoa from the Aragonese siege and then helping the Doria coup d'etat. His forces soon also besieged Mantua and Pisa, while the Venetians were badly beaten at Bergamo, which then defected to the new "Duke of Milan", being, after all, a Milanese possession less than four decades ago.
Despite attempts to relieve it, Rome remained under siege for 1462; but regardless of the Ottoman efforts, it has held out. The Pope, in another moment oft-exaggerated by those future playwrights I love to rant about, personally supervised the defenses, or involved himself in the supervision anyway. This was the Papacy's toughest hour, but also, perhaps, its finest, as the new Pope, Pius II, rapidly grew in popularity as the "Crusader Pope". Though not Eugenius, or even an ordinary genius for that matter, he used the Siege of Rome quite well to rally the Christian world around him. Poland-Lithuania still refused to send any but the most token of support, but many szlacht men volunteered, and brought their levies with them. Hungary pressed on in the Balkans, while volunteers from here also went to gather at Padua. The Italian peasantry rose up behind Turkish lines, and Venice, perhaps more out of fear of Ottoman victory rather than out of piety, donated vast sums of money to the war effort, and decimated, with token Aragonese help, the Turkish fleet in a decisive battle at Capo Santa Maria di Leuca. The Holy Roman Emperor, despite his problems with resistant vassals back at home, also sent troops, including the famed Swiss pikemen that showed themselves quite well in the eventual Battle at Rome. Even the Plantagenets, who were alittle too busy slaughtering their fellow Christians to deal with the Turks, contributed a sizeable force under the good Duke of Poitiers, Crown Prince Charles Plantagenet, which, though not reaching Rome itself, helped much against Louis II. Needless to say, the Aragonese had also contributed much to the eventual victory. Castillian hidalgos also volunteered, finding the gradualy conquest of Grenada back at home way too boring.
In 1463, Louis II's empire begun coming apart under enemy blows. Oh, he had dealed with the external ones quite fine; although the Duke of Poitiers has taken Lyons and Grenoble by the end of the year, elsewhere his forces were victorious, besieging the Venetian-held city of Brescia and, after the fall of Pisa, investing Florence itself as well. A combined army of Central Italian princes, the Venetians and the assorted mercenaries was beaten at Molozzana. Yet his forces were increasingly overstretched, and treachery also greatly damaged his cause. The Duke of Poitiers was greeted by Dauphinian nobility and urban folk alike as a liberator; peasant risings raged in the conquered territories; and the Dorias, seeing that the tides are beginning to turn, defecte to the Aragonese and provided the remnants of the Genoese fleet to them in exchange for autonomy. In 1464, having foiled numerous assassination attempts, Louis II was betrayed and killed during an attempt of capture in the Battle at Empoli. By 1465, his empire had come apart; Corsica and Liguria, indeed, became Aragonese possessions, Savoy was recreated and entered a personal union with Dauphine, while Provence became a vassal state of the Savoyards, ruled by the de la Maine dynasty (this strenghthening of the Savoyards was a result of much bickering in Milan (where the post-Louisian War peace treaty was hammered out), which clearly displayed the detirioration of Platagenet-Aragonese relations, the former wishing to gain a greater foothold in southern France and the latter wishing to minimize the Plantagenet access to the Mediterranean Sea; this Greater Savoy was intended as a buffer state). Eastern Milanese lands and Mantua went to Venice, which also reclaimed Bergamo; the rest of Milan regained independence under a Torriani pretender.
But in 1463, there were much more important events afoot aside from that. After Capo Santa Maria di Leuca, the Aragoense landed in and recaptured Otranto and Naples. Massive crusader forces were coming by the sea across the Western Mediterranean, from the north (from Padua, the main crusader gathering point) and now from the south as well. Mehmed II had no choice but to launch a general assault on Rome. Weakened by artillery bombardment, the Roman walls were assaulted and taken by the Janissaries, but only with appaling casualties. Yet there was no retreat, so Mehmed II pressed on. His forces broke into Rome itself, but the Pope made good use of barricades and the fanaticism that had been aroused in the city population to halt and force back the enemy somewhat. After two days of skirmishes, the Ottomans, having rested, resumed the assault, but it too has failed to secure all of Rome, Vatican, most notably, still holding out. Mehmed II decided to rest and try to starve his enemies out, but the anti-Turkish crusading forces had then converged on Rome. Mehmed II himself and a few of his loyal Janissaries managed to escape, but the rest were killed or captured after a brutal battle in and out of Rome.
And in the Balkans in the same year, an Ottoman counter-attack on Smederevo was defeated by Matthias, who went on to subdue much of northern Serbia and Herzegovina. A Venetian expedition got some moderate Albanian support and secured the territory, though in 1464, decimated by disease and a new Ottoman invasion, the Venetians had to pull out.
Mehmed II himself was tracked down and captured outside of Bari, the last Italian city where Ottoman presence, how ever minor, lingered. However, despite some proposals that he should be executed, Mehmed II was taken captive. When asked to concede all of his conquests, he refused but was kept alive.
Had the crusaders struck against the Ottomans in full force now... perhaps they could have brought down their empire once and for all. But as it was, they thought it not to be an urgent concern; they hoped that it will soon begin to crumble anyway. Venetians did re-invade the Aegean and once again landed in Albania; and the Hungarians did press on in Serbia, though not very decisively having come into conflict with Vlad III Dracula who did not much preffer Hungarian hegemony to the Turkish one. But the Ottomans were soon reorganized by Mehmed II's brother Orhan (OOC: in this world, he did not flee for Constantinople, instead agreeing to reocgnize Mehmed's ascendance in exchange for an important military post) and the new Graeco-Turkish buerocratic elite. Orhan did not officially claim the title of Sultan, but he was not particularily eager to have his brother come back, especially as the price of such vast territorial concessions. So instead, he continued the renovation of Constantinople, rebuilt, with the help of Genoese advisors, a navy, and levied more troops to whom he had promised land in the Balkans. The Venetian fleet was defeated at Galipoli; the Hungarians, unable to overcome the fortifications of Nish and weakened by an outbreak of a plague, fell back for Smederevo and Belgrade. But it was not the military strenght that saved the Ottoman Empire - indeed, its military was quite weakened by Mehmed's opportunistic invasion. The crusaders - much as Orhan expected - soon begun bickering after the victory in Italy. The Plantagenets had their aforementioned complications with the Trastamaras of Aragon. Venetians begun carving up the unkilled bear of the Ottomans with Aragon. Laszlo Hunyadi was increasingly challenged by the magnates and the pro-Habsburg nobility at home, not to mention the Habsburgs themselves, the Jagiellons with their Danubean ambitions and, ofcourse, Vlad III Dracula. The latter was the first to back out, seeing that the Ottomans had other things to do instead of attacking him; eternal peace was sworn, and Vlad III turned around to deal with his boyars and to prepare for a Hungarian invasion that was, indeed, inevitable (but delayed by Vlad's betrayal and the war in Serbia). The Hungarians stole Mehmed II from the Venetians (who were holding him previously) in 1466, and signed a good deal with him, letting him go in exchange for cession of the formerly-autonomous northern half of Serbia, Herzegovina and Bosnia. Orhan, recognizing this treaty as he wanted to concentrate on the Aegean theatre, intercepted Mehmed II to "ensure his safety on his return to Constantinople", and after a brief discussion the somewhat humbled Mehmed II agreed to abdicate in exchange for a military command (specifically, he became one of the Ottoman Empire's first great naval commanders); Orhan thus became Orhan II.
By then, the Pope's efforts have re-arranged, at least partially, the Mediterranean portion of the coalition. Venice and Aragon have transported a rag-tag international crusader army, backed up by their own troops, to Greece. There they were, at first, succesful, even taking Athens in a daring assault, but "surprising" local hostility and Mehmed II's devastating night attack (called, quite appropriately, the Night Attack or the Battle of the Night) on the crusading fleet at Aiyina have doomed this effort. The last great action of the war, and Mehmed's greatest triumph as an admiral, was the Second, and succesful, Siege of Rhodes (1473). It was a very brutal battle, but the Ottomans, with the assistance of the Genoese and primitive naval gunpowder artillery, came out victorious. So angry was Mehmed that, after allowing the Knights Hospitaller to flee for Malta, he had them tracked down and sunk, saying that he never promised that he will actually let them get there. The war died down afterwards, leaving the Ottomans to rebuild and reorganize, Italy to similarily rebuild and become the center of the Catholic Renaissance with many destroyed buildings, especially in Rome, being replaced by new, far better ones ([insert a certain North King quote here, you know, the one about the pillaged cities]), Aragon to involve itself ever-more in Italian and Mediterranean matters as it became, with Venice and the Ottoman Empire, one of the three Mediterranean Great Powers, Hungary to come, after Laszlo II's death, under the brief, but very exciting reign of Matthias I the Bloody (or the Great) who slaughtered rebelling magnates and noblemen wholesale, kicking Hungary into an era of strong, centralized monarchy, and the Pope to gloat as his plan for global domination advanced.
Now on to the details of the post-Mehmedian 15th century.
The Plantagenet Empire, or, as it was increasingly reffered to, the Anglo-French Kingdom, was in a consolidative stage. Henry V the Great died in 1443. Henry VI had a long, quiet reign (1443-1479) during which powerful favourites, most importantly the Count of Perche (though by then the said Count was already the Duke of Orleans and of Buckingham, to the consternation of the court), ascended and were overthrown. Despite that and the simmering unrest, this was not too bad a reign for the Plantagenets, as the economy was generally strenghthened, especially commerce and agriculture, while the army, for the most part staying out of questionable continental adventures (the only exception being the Count of Poitiers' "Italian expedition"), subdued, de jure if not fully so de facto, Ireland and Scotland (though the latter retained much autonomy). The court during this time moved southwards, to Paris, much to the consternation of the English. Soon after the death of Henry VI, this spilled out into a popular Reilly's Rising and a noble conspiracy, both of which have been dealt with most severely by the former Count of Poitiers, now King Charles I. He also put down a South French rebellion. Perhaps it is, however, good for the kingdom(s) that he died so early in 1484, for evidently he had grand ambitions in Europe itself, involving, as evidenced by his diplomatic probing in Germany, his ascension as the Holy Roman Emperor. His brother Edward IV was also an active monarch, but not a one so rash; much more patient and pragmatic, he maintained the balance between his two courts - in Paris and in London - and worked to bring the country closer together, whilst stomping down on Irish rebels and building up dynastic ties with the Burgundian Valois. Edward's son Charles II, who came to power in 1493, would be the one to taste the bittersweet fruit that came from these ties. Not literally, he was not a cannibal contrary to some rumours!
In the Pyrenean Peninsula, momentous events were afoot. Long story cut short, the wars with the Turks and expansion into Italy greatly increased Aragonese influence in the Mediterranean, to the detriment of their influence in the dynastically-connected Kingdom of Castille. Instead, the Castillian Trastamaras became increasingly Anglophile, damaging the relations with Aragon further. Plans of a greater dynastic union with Aragon disappeared; instead, relations improved with the prosperous Portugal of the Avizes. After the death of Henry V the Childless (actually, the Sonless) of Castille in 1491, the long-standing Portuguese influence and the previous royal marriage of the then-prince, now-king Joham II of Portugal to Henry's eldest daughter Leonor, bore fruit as well - Joham II ascended the Castillian throne. An Aragonese-incited rebellion against him soon begun, but was defeated; a new one started in 1492, when the newly-united and newly-declared Kingdom of Iberia's court and capital were moved to Lisbon. It was more serious, but the Iberians cracked down on it too.
The Aragonese Trastamaras were not amused, but they were too busy in the Mediterranean and agreed to recognize the new royal couple. The Treaty of Tordesillas was signed; the Aragonese withdrew all claims on Castille, instead getting Iberian neutrality in Aragon's dealings with England and the partition of the Barbary Coast, Morocco being in the Iberian sphere, and everything east being in Aragonese sphere. The Iberians continued the wars with the Moors left unfinished by both of the nations that were united to create this new one - by 1500, Grenada was subjugated with a good use of artillery, and Morocco, broken by wars, forced to pay tribute. The Iberians, meanwhile, were also enriched and strenghthened by their daring operations in Africa and in the Indian Ocean, which they were only beginning to infiltrate at the time.
As for Aragon, it just continued to become ever more prosperous from the trade and to fight the Berber pirates and the rebellions Italian vassals.
Valois Burgundy was also positively dull in these times. Phillip IV (r. 1474-1501) has led the strenghthening and centralization of the grand duchy to the logical conclusion, and defeated a heretical rising of Flemish craftsmen in late 1490s. Lorraine, through military campaigns and diplomacy, was added to the Burgundian possession, with the help of Habsburgs.
Indeed, the Habsburgs were getting ever stronger. The rule of "Bella gerant alii, tu felix Austria nube" was still working, as was the one about manipulating elections when just marrying wasn't enough. After the death of Ladislas V of Hungary, Bohemia was added to the main Habsburg possessions. Of far more long-term importance were royal marriages with Aragon (an useful ally) and, even more importantly, Burgundy, which was vital to the Habsburg plan of Imperial Reform (basically, a plan to moderately centralize the Habsburg-dominated Holy Roman Empire under their control). Since Friedrich III, all the Habsburg Emperors tried to enforce just such a reform, but their efforts were resisted by central and northern German princes; but between Austria and Burgundy, they will have no choice but to surrender. Admittedly, the Habsburgs hadn't many friends apart from Aragon and Burgundy - Venice and the Pope were vaguely allied with the Habsburgs, but relations were increasingly strained, and Hungary and Poland-Lithuania were utterly unreliable, not to speak of those perfectly wretched Plantagenets who, as Emperor Maximillian II (r. 1496-1512) raved while insane, probably still nourished their dream of winning the Imperial elections.
Venice, for a power officially victorious in the war against the Ottomans, has been badly short-changed, having only lost land and vital trade links. The city was in stagnation and decline, as was its trade network, and only the lack of serious competition kept it a trade center. Iberian invasion of the Indian Ocean, however, made things increasingly difficult...
The Papacy, despite the war's devastation, emerged only stronger from it, retaking land and, more importantly, influence. Central Italy was dominated by the Papal-Florentine alliance. The Byzantine setback was regrettable, but the Papacy, with Hungarian help, had gained Romania for the Catholic Church, and with Polish - Southern Rus (i.e. Ukraine).
The Kalmar Union, in its distant north, was cheerfully marching to oblivion as the kingdom was torn by social strife and occasional Swedish risings; however, the Kalmarese commerce begun to recover in the North and Baltic Seas as the English were distracted by the southern direction of commerce, while the Hanseatic League crumbled and declined, and Hans I put down Sten Sture's and other rebellions against his rule.
Casimir IV, while passive in foreign affairs, was very active in domestic ones, working to strenghthen royal authority and to Catholicize the largely-pagan Lithuanian lands, and the Orthodox Russian realms, where the official hierarcy, at least, accepted the Union of Florence, though a popular neo-Orthodox movement inspired by the Muscovites soon emerged. He also ensured the subjugation of the Teutonic Knights. In the south, though, he was not quite as succesful, having found himself a bad enemy in Matthias the Bloody of Hungary, who defeated both Vlad III Dracula and conquered Polish Moldavia, resisting all Polish attempts to retake it and briefly taking Lvov (thankfully, Matthias soon enough was killed there by a son of one of the countless nobles that he had "wronged" by killing).
Hungary, as mentioned before, underwent forceful centralization under Matthias I, who had also showed himself well on the military field, conquering both Wallachia and Moldavia. Although his domestic policies were ruthlessly efficient and his military efforts were brilliant, diplomatically Matthias I left the country (after his death in 1485) in semi-isolation, as the Habsburgs and the Jagiellons alike were at the knives with him, as were, ofcourse, the Turks. The centralization also claimed the lives of many nobles and magnates, leaving Hungary a bit short on educated cadres while the new buerocracy was yet being picked out. Mismanagement and corruption after Matthias' death made Hungary pretty vulnerable, despite Janos II's capable diplomacy that kept it afloat for now.
The Ottoman Empire, under Orhan II and later under his son Mehmed III (r. 1488-1523), underwent a more moderate program of modernization. The Ottomans had subdued all of Anatolia under Orhan II, as for Suleyman he had reformed and modernized the Turkish army, and campaigned against the Mamlukes in Egypt and the Ak Koyunlu in Persia, conquering the former (but allowing them to retain some power in Egypt itself, under Ottoman supervision ofcourse) and shattering the latter (having also taken Iraq from them). Persia descended into anarchy, allowing Suleyman to grab a large part of Aizerbaijan as well. On the sea, the Ottomans were less fortunate, however - the Venetians held on both to Crete and to Cyprus, and raided into the Aegean frequently. Matthias I's antigonization of his neighbours was a welcome break - Hungary had to watch its back and thus did not dare press further into the Balkans, Poland-Lithuania was too busy fighting Hungary and Muscovy, not being even able to punish the Ottoman Tartar vassals in Crimea for their incessant raiding, and the Habsburgs had no way to reach the Ottomans even if they wanted to. However, towards the end of 15th century things were moving towards a war again. Hungary begun to reconcile with its enemies, and said enemies begun to grow more united. Ottoman influence in North Africa came into conflict with Aragonese ambitions there. And in a sudden flanking move, Iberia, though rather more neutral than otherwise in the wars of Turks and the Mediterranean Christians, has entered the Indian Ocean. The Ottoman Empire was increasingly surrounded by a circle of enemies, though for now, at least, Persia was not a threat and neither were the Caucasian or Tartar tribes and principalities. And decisive action was needed to break out of it. Before such action could take place, though, an ally was needed. None could be found in Italy, obviously enough. Plantagenets were fairly neutral and maybe could even make allies out of necessity by the principle of an enemy of one's enemy being an ally. The Barbary Coast states were natural allies, or rather vassals, but apart from pirates and distractions they were of no use at all. An ally was found via the Patriarch of Constantinople, though...
Ivan III, the Velikiy Knyaz of Muscovy, had been carrying out yet another centralization program. He was greatly inspired by the Ottoman Empire, especially by the way the clergy was subservient to the Sultan. He also was quite anti-Catholic, quite reasonably because the pro-Florentine clergy in Russia - the more important of its hierarchs, anyway - was extremelly Polonophilic, and in Polish- (well, Lithuanian-) held territory formed one of the pillars on which Jagiellon power rested. So Ivan III took strong measures against "Florentianism", denouncing the results of the Council altogether during one of his brushfire wars with Poland-Lithuania. But he did not want the Orthodox church to continue as before. So he reformed it, with the help of the "nestyazhateli" puritan faction. The church was put under state control, de facto; and all its lands were confiscated by the Knyaz, to avoid the clergymen "falling into sin". The Metropolitian of Moscow, Iosif, has tried to fight back, by arranging a conspiracy of the nobles (which backfired, as after the executions the Knyaz was more powerful and feared than even before) and trying to incite peasant risings, which did not occur on a large scale due to the fair amounts of contempt accumulated by the peasants towards "the popes", as ignited by Nil Sorsky, the leader of the nestyazhateli and the new Metropolitian. On the wave of the religious revival ignited by this, Ivan III managed to tear a few borderlands out of Lithuania, and to conquer Kazan'. An obvious enemy of the Catholic Europe, Muscovy had established an alliance with the Crimean Khanate - a Turkish vassal - against the other Tartars. This allowed the Ottomans to create an alliance with Muscovy, how ever informal at this stage.
Thus as the 15th century closed, numerous conflicts and enemities within and outside Europe were moving towards violent, bloody resolution in an all-out, decisive clash. In such a situation, who the hell would care about some mad Genoese expatriate and his ideas?! Who needed the western route to India, or indeed Transoceania itself with all its riches and venereal diseases, when there were wars to be fought and colonies to contest? Who? Nobody. There you go Andis, on to the 16th century and lots of blood-shed whenever I find the time for it.