They say Rome wasn't built in one day... But neither was Carthage. Brilliantly outmaneuvering Scipio Africanus, Hannibal the great realized that he won't last long away from home, now that some of his loyal soldiers apparently joined the enemy's ranks. He returned to the city of Carthage as victorious against the seemingly unbeatable romans, but didn't waste his time parading. He had no reason to: he knew the Romans won't stop until Carthage will be destroyed. He than marched onto the desert, forcing the Numidians to swear allegiance to Carthage. Those who resisted him were murdered; but that wasn't enough for him: in what took him nearly 5 years, he marched through Iberia, claiming the subcontinent for his own empire and making its residents Carthaginian citzines. This "Pacification" of Iberia laid the foundations for the Carthaginian empire that would emerge some 500 years later... By that time, Carthage had control of entire north Africa, and had the strongest army of its time under her control; an unstoppable war machine, not due to its size, but due to its many, many different troops: from Iberian slingers to Forest elephants, the Carthaginian army could organize itself in whatever position it wanted, and could win a fair(or unfair) battle almost everywhere. The Romans, on the other hand, never really recovered since their defeat... The Legion's armor was nearly doubled in weight since the end of the Punic wars... Rome spent most of its resources fortifying its borders, looking to defend themselves from the southern menace. You could almost say that while Carthage excelled on offence, Rome was just as good in defending itself. Before the events that shook Europe, which I will describe soon, Rome controlled most of northern coast of The Mediterranean. Not exactly "Mare Nostrum", but you could see Roman vessels patrolling their from time to time. The two empires actually became besties(well, not really. Occasionally checking who is better at spear throwing is better than an all-out war, right?) And there was a direct trade route between the two great cities...
But than came Attila, and the sight of destruction caused by his forces certainly inspired the nightmares for the leaders of the two empires. Suddenly, tribes came knocking down the huge walls of the Roman Fortresses, seeking Asylum after escaping from God's scourge. But the God's will is not to be denied, and soon the Huns broke through the Roman lines as well.
But some tribes migrated further. Carthage had to deal with rather warlike tribes, raging beasts who looked for vengeance after witnessing the true horrors of war. Unlike the Romans, who tried to make those tribes part of their society(and ending up doing the opposite) the Carthaginians were more open minded: they knew that they'll eventually clash with the Romans, and they knew that if they attack Rome alone, now, they run the risk of ending the same way Rome did: With countless enemies, both on the inside and the outside. So, they came up with a plan: they paid the tribes, trained them, gave them some more sophisticated weaponry, and essentially set Rome ablaze: The Roman navynwas now destroyed. Carthage has penetrated the eastern border, after participating in the Partition of Asia minor with the Persian empire and the Barbarians made their own trail of destruction leading all the way to Rome.
Carthage went down in history as a nation who didn't fight many wars but defeated most of its enemies... Many after taking control of the northern coast, many great reforms were made: Cothon style ports appeared in every province; Road systems were built throughout The European and African Coasts, allowing the army to move swiftly and quickly get to any part of the empire.
The empire didn't last long past its golden century: A rebellion in Iberia marked the decline of the empire, culminating in a siege of the capital city by Numidian tribes. The city itself was never conquered though, and serves as its own capital up to the present day.