The third Punic war began in 149 BC and lasted intill 146 BC. The entire war was nearly just Carthage defending its self and as Rome’s rath fell on Carthage in full force the city could do nearly nothing.
So the way this war started was that as Carthage slowly recovered after the second Punic war (which it lost) Rome thought it neaded to just be destroyed and not punished. A famous Roman senator named Cato the Elder ended every speech with “Furthermore it is my opinion that Carthage must be destroyed” and he said that even if the speech had nothing to do with Carthage. Now there where some reasons for Rome to get mad at Carthage not just because they thought they should destroy the city but Carthage broke a treaty when in 151 BC Numidia attacked Carthage and Carthage won. How Carthage broke a treaty was that it raised a army to defend itself .This was not allowed by the treaty after the second Punic war and so Rome attacked Carthage in 149 BC. Carthage tried to get Rome to make peace but Rome wouldn’t listen and in 146 BC Carthage fell. The city of Carthage was destroyed entirely and salt was poured on the ground so crops wouldn’t grow well there. This would seem like the end of Carthage and it was for the original Carthage but Julius Caesar rebuilt Carthage in to a Roman city. The city was of course under Roman control but it was soon after that the main political and trading hub of Roman Africa.
The city of Carthage has had a lot of things happen in its short life time it rose to be the most powerful nation in the Medirtan and in fell just as quickly as it rose.