Hannibal sacks and defeats Rome
After Hannibal's victory at Trebia in 218 B.C. and at Lake Trasimene the following year, Hannibal began to rethink his strategy, which was essential a giant raid of Rome. Initially, Hannibal thought a few striking victories would cause Rome's allies to break with Rome and cause the Romans to sue for peace . Now, Hannibal became convinced that this would truly be a fight to the death, and to ensure the survival of Carthage, Rome itself must be destroyed. Hannibal took to ending all of his councils of war with the phrase ' Rome must be destroyed.'
However,Rome was well defended with massive walls and Hannibal had no siege equipment .While Fabius sought to wear away Hannibal's forces through guerrilla warfare, Hannibal had some lucky breaks. Phillip V of the powerful Hellenistic Kingdom of Macedonia threw his lot in with the Carthagians, and harassed Roman costal towns. More importantly, he was able to send engineers and some siege equipment. The revolt of Syracuse against Rome permitted Carthage to land major reinforcements to Hannibal in south Italy and Archimedes designed new and more powerful catapults for Hannibal to use .Hannibal had been trying to goad the Romans to give up Fabius' tactics, but also himself avoided a major battle till his siege equipment was ready. After Hannibal's victory at Cannae, Hannibal sent a small force of Carthagians and Greek mercenaries ahead to march on Rome, which caused panic and many Roman allies to side with Hannibal. Rome recalled the Scipios from Spain to relieve the siege of Rome, but arrived too late .After months of siege, Hannibal was able to take Rome and the city was sacked . Those Romans who were not killed were taken as slaves to Carthage .Today there are few remains of the city itself .
A large Carthaginian force remained in Capua, the capital city Magna Graecia an became, over time the most powerful city in Italy. Carthage became the major power in the western Mediterranean under his rule and that of his sons. After the death of Hannibal's' son, the army reforms of Hannibal were abolished and Carthage returned to the cheaper mercenary system. Carthage was defeated by the Ptolemaic Kingdom after entering into an alliance with Selucid kingdom. the Punic kingdoms in Spain then grew in power. After the fall of Rome, no one city state was able to reunite Italy as Rome had done. The Selucid Empire briefly ruled large parts of Italy, till the rising Sassanid Empire weakened forced it to withdraw its forces. Much of Italy was then overrun by Germanic tribes .(still working on this, trying to imagine a future timeline where the Roman Empire did not exist)
John Maddox Roberts's alternative history Hannibal's Children is an interesting expedition to answer the question "What if Hannibal of Carthage had succeeded in his bid to conquer Rome during the second Punic War?"