This war was a much smaller engagement than the two previous Punic Wars and focused on Tunisia, mainly on the Siege of Carthage, which resulted in the complete destruction of the city, the annexation of all remaining Carthaginian territory by Rome, and the death or enslavement of the entire Carthaginian population. The Third Punic War ended Carthage's independent existence.
In the years between the Second and Third Punic War, Rome was engaged in the conquest of the Hellenistic empires to the east (see Macedonian Wars, Illyrian Wars, and the Roman-Syrian War) and ruthlessly suppressing the Hispanian peoples in the west, although they had been essential to the Roman success in the Second Punic War. Carthage, stripped of allies and territory (Sicily, Sardinia, Hispania), was suffering under a huge indemnity of 200 silver talents to be paid every year for 50 years.
According to Appian the senator Cato the Elder usually finished his speeches on any subject in the Senate with the phrase ceterum censeo Carthaginem esse delendam, which means "Moreover, I am of the opinion that Carthage ought to be destroyed". Cicero put a similar statement in the mouth of Cato in his dialogue De Senectute. He was opposed by the senator Publius Cornelius Scipio Nasica Corculum, who favoured a different course that would not destroy Carthage, and who usually prevailed in the debates.
The peace treaty at the end of the Second Punic War required that all border disputes involving Carthage be arbitrated by the Roman Senate and required Carthage to get explicit Roman approval before going to war. As a result, in the 50 intervening years between the Second and Third Punic War, Carthage had to take all border disputes with Rome's ally Numidia to the Roman Senate, where they were decided almost exclusively in Numidian favour.
In 151 BC, the Carthaginian debt to Rome was fully repaid, meaning that, in Punic eyes, the treaty was now expired, though not so according to the Romans, who instead viewed the treaty as a permanent declaration of Carthaginian subordination to Rome akin to the Roman treaties with its Italian allies. Moreover, the retirement of the indemnity removed one of the main incentives the Romans had to keep the peace with Carthage – there were no further payments that might be interrupted.