They - like many Germanic tribes before and after them - migrated westwards, possibly due to attacks from the ever-approaching Huns. They traveled west with their allies, first along the Danube and then coming in contact with the tribes living along the Rhine. After defeating them they went on to cut a destructive swath through Gaul, looting their way south and west until they crossed the Pyrenees.

At this point, there were two tribes that had been part of the migration: the Vandals, which were themselves split into two different groups that we won't name for simplicity's sake, and their allies the Alans. The Roman Emperor at the time could not stop them, and so he offered them various lands in Spain in exchange for peace.

However, the Visigoth tribe, which had invaded Spain earlier and had been also been offered land by the Romans, defeated and utterly crushed the Alans not long afterwards. So that Alans turned to their old ally the Vandals, and the Vandal king took the crown of the Alans (styling himself Kind of the Vandals and Alans). However, even while being united the two tribes faced severe opposition in Spain from both the hostile Visigoths and especially from a powerful Roman-Suebi coalition. Thus the Vandals once again packed their bags and left in search of safer pastures, crossing into Africa some 20 years after they first left the eastern bank of the Danube.

From there it would take another ten years before Carthage would fall in their hands, and from there the Vandals would finally settle down and build a powerful state that would resist Roman attempts to reconquer it for another century or so.