The Civ3 barbs are simple; aggressive, destructive, an obstacle to the human player or AI on their way to victory. For other games in the franchise, the developers have added new traits. In Civ4, I've seen barbs take over cities, make lots of units, and become a more difficult obstacle for the human player. Both Civ5 and Civ6 introduced city-states: small, single-city sendentary minor entities who are not trying to win the game. They can be interacted with, traded with, enlisted to help in wars. In Civ6 (I've stopped playing Civ5, so I can't say for certain), the city-states do have a technology path and improve their units. In the Civ6 base game, both human-led and AI-led major civs can pay a city-state to command their troops as a supplement to one's own in a war; the in-game term is "levy" their army, for 30 turns.
An optional Civ6 game mode is called "Barbarian Clans", where the player has even more options than simply killing the barb units and clearing their camp. One can buy a unit from a clan, or bribe them to be less aggressive or to harrass a neighbor.
Some of the ideas we mentioned here are already being tested.