Short answers, pulled from the story.
The Vandalic War was a military conflict fought in North Africa between the Byzantine Empire and the Vandal Kingdom from 533 to 534. It was the first war of Emperor Justinian I's campaign to reassert Roman sovereignty over former Western Roman territory, and it ended with the complete defeat of the Vandal Kingdom and the restoration of Roman rule in Africa.
General Belisarius commanded the Byzantine expeditionary force. Justinian selected him for his military record against the Persians, his knowledge of Latin, and his reputation for maintaining discipline among his troops. His secretary Procopius accompanied the campaign and wrote the main historical account of the war.
The Battle of Ad Decimum was fought on the 13th of September 533, the tenth day of the march from Cape Caputvada. The Vandal king Gelimer planned a three-pronged encirclement, but the three forces failed to coordinate. His brother Ammatas was killed before the trap could close, and his nephew Gibamund's flank force was destroyed by the Hunnic cavalry. When Gelimer came upon his dead brother's body, he halted the battle; Belisarius used the interval to rally his cavalry and rout the Vandals.
Gelimer had dispatched 120 warships and 5,000 men under his brother Tzazon to suppress a revolt in Sardinia just before the Byzantine fleet arrived, removing both his navy and a large portion of his army from Africa. The Vandal army was also composed exclusively of lightly armoured cavalry with no archers, placing it at a structural disadvantage against Belisarius' cataphracts and horse archers.
After surrendering in the spring following his blockade at the mountain stronghold of Medeus, Gelimer was brought to Constantinople and paraded in a triumph at the hippodrome before Emperor Justinian. He was given an estate in Galatia and offered the rank of patrician, but refused the honor because it required him to renounce his Arian faith.
The triumph in Constantinople included the Vandal royal treasury, which contained objects looted from Rome 80 years earlier including the imperial regalia and the menorah of the Second Temple. Gelimer himself was paraded in purple robes before being forced to prostrate himself before Justinian. Belisarius was later named consul ordinarius for 535 and carried through the streets on a consular chair held aloft by Vandal warriors.