When the First Punic War ended, Rome forced Carthage to accept responsibility for starting the war. As a result, Rome took Sardinia and Corsica off Carthage - which was totally illegal under the Peace agreement signed by Rome and Carthage.
The taking of Sardinia and Corsica has been argued by many leading historians and the writings of Polybius, that it was this that started Rome on the road to Empire.
However, Carthage did not see Sardinia and Corsica as part of the agreement and would be one of the major resentments of Carthage to go to war again - which Rome narrowly won.
When the Second Punic War ended, Rome forced Carthage to give up her commerical empire and destroy her navy - it gave Rome total control over the Mediterranean.
While the war gave Rome control of Africa, Rome used the war as a pretext to go after another one of its enemies - Philip V of Macedon, who Rome found had promised Cathage help against Rome. Demanding Macedonia's total surrender, Rome marched into Macedonia and allowed Rome to claim hegemony over Greece from Macedon.
WIth total supremacy, Rome used a flimsy pretext to totally destroy Carthage. When Carthage threatened to rebuild its walls, Rome used it as a pretext to declare war, destroy Carthage to the ground and force Carthage into slavery.
It is the Punic Wars that mark not only the Rise of the Roman Empire, but the fall of the Republic - famous Roman consuls (generals) as Scipio Africanus served not only as consul once but several times.
It also marked the rise of the Demagogue in Roman Politics - the famous Roman tribunes Tiberius and his brother Gauis would rise to prominence to fight for land distribution among Rome's allies - and would be murdered by the conservatives of Rome.
It also marked the rise of a dictatorship in times of Crisis - something which Roman consuls and popular politicians as Caesar would use to their advantage.
