I am Hungarian, and ancient Hunnish/Hungarian history is kind of my are of expertise as well...
Are you a historian?
I have access to many sources (listable, if you like) which have simply not surfaced outside of Hungary.
I am quite comfortable reading Hungarian, and with four (of five) years in a Hungarian university studying history and ethnography (néprajz) I won't have any trouble accessing your sources. I'll freely share my own of course.
The Hungarians and Huns can be most accurately traced back to Crimea in the Black Sea, where they developed into their nomadic tribes and moved north-east past the Urals.
The Huns did not develop in the Black Sea area; they enter history in the 3rd century B.C. as the Hsiong-nu who harassed the nascent Qin Dynasty of China, living just north of modern Beijing. It was to defend themselves against the Hsiong-nu that the great emperor Qinshihuangdi began building the first battlements that would evolve in later centuries to become the Great Wall.
While in the latter centuries B.C. the general Steppe lifestyle was developing, it is a great mistake to assume that it was one uniform culture, though it often looked that way to the settled "civilized" peoples who lived on its perimeters and suffered its ravages, like the Chinese or the Byzantines. The Huns were only one among a great variety of Turkic peoples, for instance, belonging to the eastern "Mongol" Steppe Turks with little relation to the later western Turks (like the Avars or Khazars). Also, as I so often like to point out, it is a mistake to impose backwards through history our modern notions of ethnicity; being a "Hun" meant belonging to a tribe or tribal confederation, and involved peoples speaking many different languages but owing loyalty to a common clan and goal. At its height the Hunnic empire in the mid-6th century A.D. stretched from the lower Volga to the Carpathian Basin but as with all Steppe empires these were in reality administered by conquered and allied tribes along the way. European, Chinese and Indian sources all describe the Hunnic armies as consisting of large numbers of non-Huns; in Europe they described various Iranians, Slavs, Germanics, etc. This was quite normal in Steppe armies.
In any event, part of the Huns split off and moved northwestward in the late 1st century A.D. towards the Aral Sea and Lake Balkhash after a civil war within the Hsiong-nu empire. It isn't exactly clear why this group moved westward and Chinese sources are mum, but move they did and in the late 4th century these Huns exploded into the western Steppe by attacking the Alans, the Ostrogoths and Visigoths.
This is the time we begin to see Huns along the Black Sea shore, many centuries after their inception along the northern Chinese cultural periphery. The Huns followed the Alans, Ostrogoths, and Visigoths into the Danube Basin, and crossed it in A.D. 441 (under Attila's leadership) to begin "their bit in Europe", ravaging about until the withdrawal from Rome in A.D. 452 and Attila's death afterwards.
The Huns did their bit in Europe, then split up, some returning to the Urals and the others settled down in Transylvania.
There is a partial truth here, but not completely. The Huns after Attila's death did indeed split up with some accepting Byzantine hospitality and settling in what is today Bulgaria (Moesia) but the group that moved eastward did not maintain unity. Quite the opposite in fact; it split into two main groups, the Kutrigur Huns and the Uturgur Huns. The Kutrigur settled around the Sea of Azov, while the Uturgur established themselves at the mouth of the Don River. These groups fought each other incessantly, until both were destroyed by the Avars in the late 6th century. Note that neither were anywhere near the Urals. The survivors of the Avar onslaught were absorbed into the new Avar empire which was marching steadily westward, towards of course the Danube Basin where it would hold sway until being destroyed by Charlemagne in the late 8th century. History does not record anything more of the so-called "western Huns" (i.e., those who fled westward to the Aral Sea in the 1st century).
For much of this I used a couple basic sources, especially René Grousset's excellent 1970 book
The Empire of the Steppes, a History of Central Asia. To a lesser extent: E.D. Phillips'
The Royal Hordes: Nomad Peoples of the Steppes, with brief help from Lucien Musset's
The Germanic Invasions, The Making of Europe 400-600 A.D. and John Fairbank and Merle Goldman's simple
China, a New History. However, though I usually shy away from web sources I did find some helpful information
here.
Now, the Hungarians:
The Hungarians and Huns can be most accurately traced back to Crimea in the Black Sea, where they developed into their nomadic tribes and moved north-east past the Urals. From there, we lost track of the Hungarians, but they surface many times in Hun records and legends.
"Hun records and legends"? Problem: The Huns were an illiterate people who left no records. Linguists today argue over the early splits in the Altaic languages largely because they - the Huns among them - left no written evidence of their languages. It is reported that the Chinese had some who could speak with the Huns but we don't know if they spoke Hunnic, or another third neutral language, or Chinese. For instance, the Hunnic names of their leaders that we have
all come down to us through other sources, meaning they have been bled through the transliterations of other Turks, of Chinese, Arabs, Slavs, Byzantines and Europeans. We do not know how Attila may have actually pronounced his name, or if we have his name correct. The website I sited mentions an early Turkic "Orkhon" script but no samples written in Hunnic survive today. Simply said, there are no "Hun records", unless you're thinking World War I-era German music.
Your one saving grace in finding any Hun-Hungarian connection may be with the Onogurs, the Bulgaro-Turkic khanate that ruled in the Kuban region briefly in the 7th century. There is one theory (though quite controversial) that the Onogur Bulgars were descendants of the Huns, though this is unsubstantiated and the origins of the Bulgars has been more credibly linked to the Pamirs (look to the modern Chuvash). Even if there is some truth to the Onogur Bulgars having either descended from or absorbed the remaining Huns, the physical evidence (i.e. burials) shows a clear distinctive western Turkic style unknown to the Huns of Attila's day.
But back to the Hungarians:
Between A.D. 700 and 750, the Magyars moved southwestwards from "Magna Hungaria" (modern Bashkiria in the Urals) towards Levedia (c. 800) in the northern Caucasus, around the mouth of the Don River, which was peopled mostly by the remnants of the Iranian Alans and ruled by the Turkic Khazar empire. After the Khazar civil war of the 820s, the Magyars edged westward towards the Dniepr River along the Black Sea coast, known to them as "Etelköz" (Between the Rivers) where they were established by c. 850. They had already been doing mercenary work for various Christian Europeans since the 830s and knew the Danube Basin fairly well. When in the midst of a war with the Bulgars (situated in modern Bulgaria) the Magyar homeland was attacked by the dreaded
Besenyök (Pechenegs) in 895, the Magyars straggled rather unheroically and desperately into the Carpathian Basin - contrary to heavily romanticized versions of mighty Magyar armies roaring through the Verecke Pass in the
Honfoglaló. Though the year 896 is traditionally celebrated as the year the Magyars seized their current homeland, most historians (Hungarian included) agree that it took the Magyars a good century, to almost A.D. 1000, to fully control the traditional Hungarian lands from Transylvania to the Rába.
Anyway, the Hungarian people followed the Huns down 400 years later to find the "promised land" the returning Huns spoke of. They found the Carpathian Basin, Hungary, and after some brief feuds settled down, in cooperation with the Szekelys in 896 AD.
Well, the Magyars did not follow the Huns as there were no Huns to follow by the late 9th century. Remember that while the Huns are a gigantic people in Western History, there were just another Steppe empire for the peoples of Central Asia. Their reach and destructiveness made them legendary in Europe, but they were shooting stars for the peoples of the Black Sea, the Caucasus, the Caspian, etc. By the time the Magyars showed up on the Black Sea, the Huns were ancient history. The grasslands of the Carpathian Basin were known to many of the Steppe peoples (Gepids, Goths, Dacians, Bulgars, Avars, etc. etc. etc.) and was a known route into Europe.
The Huns did their bit in Europe, then split up, some returning to the Urals and the others settled down in Transylvania. THEY ARE STILL ALIVE TODAY, called the "Szekelys" and consider themselves Hungarian. The most obvious link to their Hunnish heritage is the referance to Csaba, Atilla's son, in their anthem.
This is a highly controversial theory, that the Székely were descended from the Huns who fled southward, and by no means accepted widely by modern Hungarian historians. There are many other theories as well, ranging from the Székely being fellow Ugric travellers to being simply Hungarians displaced by medieval land redistribution and re-settled in the frontier regions as border guards (i.e., "szék-ely"), in typical medieval fashion. A critical clue to their originds is the fact that while Székely Hungarian is a dialect, it nonetheless bares according to Hungarian linguists traits of having developed steadily along with pre-"Conquest" as well as medieval Hungarian. In other words, Székely Hungarian has a historical relationship with mainstream Hungarian much earlier than A.D. 896.
In 1200 AD, a Hungarian priest decided to investigate how accurate the legends were by trying to find the Hungarians and Huns who had remained east of the Urals. He DID find them, and they warned him of a massive impending invasion force headed for Hungary.
Julián (Iulianus), who twice ventured to find the ancient Hungarians of "Magna Hungaria" did indeed find them in 1236 (interesting
article here that begins with Julián's journeys) but I'm afraid there were no Huns there. He reports that the bashkir Magyars live among the Volga Bulgars, but no Huns. Indeed, modern historians assume these Bashkir Magyars, such as survived the Mongol onslaught, were eventually assimilated into the Volga Bulgar ranks, for they disappear from history after Julián's missions. There are other groups of break-away Hungarians as well that we know almost nothing about, like the "Sabir Hungarians" who lived among the Sabir/Savir Turks of the Caucasus and are mentioned in an Arab source once. It is of course dangerous to be labelling peoples too precisely since there was no absolute atlas of who was who and where they lived in these times; for instance the Byzantines ahd a habit of labelling any horse-people who came out of the east with whom they didn't have immediate relations
Turkoi (Turks), and indeed early Byzantine sources refer to Hungarians (among others) as "Turks".
In 1250, the Tatars (Tartars, Mongols) swept through Hungary, destroying much of it. A subsequent mission to the Urals found no trace of the ancient Hungarians.
Yes, the Mongols swept through the Hungarian kingdom in 1241-42 with such destructive force that nearly 50% of the Plains population of the kingdom was killed off.
Sources:
For this I relied heavily on one of my favorites from my student days, Fodor István's
Verecke híres útján, a wonderful summation of Hungarian prehistory and all the known archaeological evidence stretching from the ancient Ugric peoples to the "Honfoglaló" Magyars. I also trotted out however Volume One of the MTA's
Magyarország Története, Elôzmények és Magyar Történet 1242-ig. I relied a bit on Gyula László's
Ö'störténetünk for some back-up and for Székely I reached for the MTA's English-language version of
History of Transylvania.
Other recommeded reading would be the popular Corvina Press English-language book
Attila, the Man and his Image (published in Hungary) which traces the popular image of Attila in the centuries after his death, and has some illuminating sections on Kézai Simon's appropriation of the ancient Scythian/Sarmatian/northern Iranian myth of the White Stag or the Magical Stag to fabricate a Hunnic-Hungarian connection in his 13th century chronicle. Fodor István also describes this dismissively.
In summation: The Huns were long gone by the time the Magyars made their appearance on the Black Sea scene in the 8th century, and while the two peoples followed vaguely a similar lifestyle on the Steppes tat so many other Turkic, Ugric, Iranian and etc, peoples also followed, the connection between them is ultimately null.
