On September 13, 533, a Roman army of about 15,000 men under Belisarius defeated the Vandal army of King Gelimer at Ad Decimum, the tenth milestone on the road to Carthage. The Vandal kingdom in North Africa had existed for 99 years, since its people crossed into the province in 429 and took Carthage in 439. It ended in two battles and a siege.
Belisarius had sailed from Constantinople with about 500 transports and 92 warships, which was a very small force for the job and was chosen partly for price. Justinian wanted the expedition. His ministers did not. The treasury was short, and the Persian frontier was active. Belisarius was 28 and had already fought the Persians at Dara.
The battle nearly went the other way, and the reason is interesting. Gelimer had planned to concentrate and attack the Romans in a narrow place with three forces at once: his brother Ammatas from Carthage, his nephew Gibamund from the flank, and himself from behind. It is a plan that requires timing, and the Vandal army had no reliable way to coordinate three columns that could not see each other. Ammatas arrived early with a small force, was defeated and killed. Gibamund's detachment was found and destroyed by the Roman cavalry. Then Gelimer, coming up with the main body and unaware of either, drove the Roman advance guard back toward Belisarius, and there stopped.
That hesitation is the battle. Had he pressed on, the Roman army was in no state to receive him; Belisarius was still behind with the main body and the baggage. Gelimer found his brother's body. He lost his nerve. He withdrew to a plain where Belisarius could deploy and the Roman cavalry could work. The Vandal army broke.
Carthage opened its gates on September 15. Gelimer was defeated again at Tricamarum in December and surrendered in the spring of 534, and he was taken to Constantinople for a triumph. Justinian recovered Africa, Sicily, Sardinia and Corsica, and then went on to Italy, where the war against the Goths took twenty years and ruined the peninsula.
Belisarius' reconquest is the largest of Justinian's wars and the only one that held. The province stayed Roman until the Arab conquests of the late seventh century.