There is yet no definitive conclusion about their ethnic affiliation. They could have been an Iberian or an Aquitanian tribe, but because of their ethnic name, and place and river names, the indo-European, pre-Celtic indo-European and Celtic affiliation possibility is more likely. They may have been a Celtic tribe, related to the Suessiones that dwelt in Gallia Belgica, northern Gallia in today's Soissons area. Suessiones tribe, that dwelt in the Marne river territory, had a city called Corbio, like the Suessetani. So there is an association between the root words suess- and corb- in these two tribes. It is not known when did they arrived in the region that they dwelt but some estimate that they arrived around 600 BCE, or maybe earlier, along with a belgic Celtic migration. Their ethnic name, Suessetani, means “Lucky People” or "Good People" from the root wordsuessio, being lucky, good luck. The Caristii tribe had a place name - Suessatio that was derived from a related word. The place names and river names of their territory are clearly indo-European, probably Celtic or pre-Celtic indo-European. The place names are for example: Corbio, Viridunum, Gordunum, Navardunum, Sekia/Segia, Setia, Gallicum, Forum Gallorum. The river names are Alba, Gallicus river. This seems to indicate that they spoke an indo-European language, maybe a Celtic one.
Roman conquest
wrote about Marcus Porcius Cato's campaigns in Hispania. In his work he reports that the Suessetani were enemies of the Iacetani, because, on other things, Iacetani sacked the fields and crops of the Suessetani. Marcus Porcius Cato, knowing the bad relations between Suessetani and Iacetani, took this to Roman advantage and managed to gain their support for the Roman conquest of the Iacetani territory and their capital, Iaca, in 195 BCE. So the Suessetani, at the beginning of the 2nd Century BCE, were Roman allies, but some years after they rebelled and resisted against Roman expansion, an action that had terrible consequences for the Suessetani as a tribe with his own identity. Because of this, their territory and capital was taken by a Roman army on the orders of the governor of Hispania Citerior, Aulus Terentius Varro, in the year 184 BCE. Corbio, the capital, had to be taken using siege weapons and was destroyed after that siege.
Assimilation by the Vascones
The Vascones, that dwelt to the northwest of the Suessetani, in alliance with the Romans and with Roman incentive, took advantage of the Suessetani defeat, they took Suessetani lands and assimilated most of them in the middle and the end of the 2nd century BCE. The Suessetani ceased to exist as a different tribe with his own identity. When later authors such as Strabo and Ptolemy wrote their works, the Suessetani had already been assimilated by the Vascones, as they don't mention them. They describe the Suessetani former territory as a vasconian one. Partially because of this, Suessetani are sometimes ignored as a different tribe or wrongly classified as a tribe of the Vascones or the Iberians.