The Third Punic War was fought between Carthage and the Roman Republic from 149 BC to 146 BC. This was the last in a series of three wars.
In the years between the Second and Third Punic Wars, Rome was engaged in the conquest of the Hellenistic empires to the east and ruthlessly suppressing the Iberian people in the west, although they had been essential to the Roman success in the Second Punic War. Carthage, stripped of allies and territory (Sicily, Spain) was suffering under a yearly indemnity of 200 silver talents to be paid every year for 50 years, an enormous sum.
The Romans still harbored a bitter hatred for Carthage, which had nearly destroyed them in the Second Punic War. Sentiments ran so strong that the powerful statesman Cato ended every speech, whatever the topic, with the phrase ceterum censeo Carthaginem esse delendam. (In conclusion, I think that Carthage must be destroyed).
Meanwhile, Carthage had regained much of its prosperity through trade, further alarming Rome that a revived Carthage could again threaten them with war.
The peace treaty at the end of the Second Punic War required that Carthage get Roman approval before declaring war; however, Carthaginian hotheads launched a war against neighboring Numidia without Roman consent. The Roman Senate secretly voted to declare war and began gathering an army. The Carthaginians made a series of attempts to mollify Rome - including sending three hundred children of well-born Carthaginians as hostages - but without success. The Romans landed an army nearby at Utica while negotiations continued. When the Carthaginians learned that Rome's final demand was that they leave their city, destroy it and rebuild 10 miles inland, they abandoned negotiations and the city was immediately besieged, beginning the Third Punic War.
The Carthaginians endured the siege from 149 BC to 146 BC, when Scipio Aemilianus took the city by storm. Many Carthaginians died from starvation during the latter part of the siege, while many others died in the final six days of fighting. When the war ended, the remaining 50,000 Carthaginians (perhaps a tenth of the original pre-war population) were sold into slavery.
The city was systematically burned for somewhere between 10 and 17 days. Then the city walls, its buildings and its harbor were utterly destroyed and the surrounding territory was supposedly sown with salt to ensure that nothing would grow there again. The sowing may have been merely a symbolic curse against Rome's defeated enemy, or the account may be entirely invented; it does not appear in the records of the war, and historians today dispute whether it actually happened.