First Punic War: Initially, Rome and Carthage were well-matched. Rome had recently come to dominate the Italic peninsula, while Carthage controlled parts of Spain and northern Africa, Sardinia, and Corsica. Sicily was the original area of contention. At the end of the First Punic War, Carthage releases its hold on Messana, Sicily. The two sides were otherwise much the same as before. Although it was Carthage that sued for peace, Carthage was still a great mercantile power, but now Rome was also a Mediterranean power.
Second Punic War: The Second Punic War started over conflicting interests in Spain. It is sometimes called the Hannibalic War in tribute to the great general of Carthage, Hannibal Barca. Although in this war with the famous elephants-crossing the Alps, Rome suffered serious defeats at the hands of Hannibal, in the end, Rome defeated Carthage. This time, Carthage had to accept difficult peace terms.
Third Punic War: Rome was able to interpret a defensive move of Carthage against an African neighbor as a violation of the Second Punic War's peace treaty; so Rome attacked and wiped out Carthage. This was the Third Punic War, that Punic War, about which Cato said "Carthage must be destroyed." The story is that Rome punitively salted the earth, but then Carthage became the Roman province of Africa.
Punic War Leaders: Some of the famous names connected with the Punic Wars are Hannibal (or Hannibal Barca), Hamilcar, Hasdrubel, Quintus Fabius Maximus Cunctator, Cato the Censor, and Scipio Africanus.