The Cheetah People had the heads of cheetahs and thick, spotted fur, distinctive golden eyes, retractable claws and sharp fangs. They also had an excellent sense of smell which they could use to track their prey. (TV: Survival) They were distantly related to the Cat-People. (PROSE: Invasion of the Cat-People)
Some of the Cheetah People, like Karra, began as humanoids, gradually acquiring the characteristics of a cheetah. Their eye colour changed to gold, the pupils gained the feline slit shape and they developed fangs. Of the Cheetah People seen, only Karra spoke, but she did so without any difficulty. At the moment of her death, Karra lost all her cheetah characteristics. (TV: Survival)
The Cheetah People had a symbiotic relationship with their world, as well as with the native kitlings. The planet was almost alive and was mentally connected with the Cheetah People. Its sources of water could heal them, and if they fought the planet would slowly start to destroy itself. The Cheetah People could also use the kitlings to find new sources of food, since they could mentally control them and see through their eyes. They had the ability to teleport from planet to planet, but they could only bring back prey to their homeworld. It seemed, even worlds away, that they knew if one of their kind had died. (TV: Survival) Even after returning to their original species, individuals could sense those who were once Cheetah People. (PROSE: First Frontier)
They also had the indirect ability to change people in their own kind. Persons influenced enough that they had started to turn into Cheetah People included: the Master, Ace, Midge and the Seventh Doctor. Karra had been deeply affected by the planet's influence, which led to a full transformation. (TV: Survival) After being cured, Ace could still draw on the Cheetah People abilities, granting her increased speed. (PROSE: Cat's Cradle: Witch Mark)
Cheetah People were a dangerous, but playful, race, with many traits associated with terrestrial felines. They were intrigued by shiny objects such as Captain Sorin's cap insignia which Ace wore on her jacket. They would only go after food which was moving and would attempt to make hunts more interesting. By human standards, they would have had a vicious way of life and would fight each other over spoils or kill helpless humans without provocation. They did seem to have some sort of respect for their own dead and would return to a world to come back for their fallen. The Cheetah People generally wore leather open-toed shoes and trophies from their hunts, using horses as mounts. (TV: Survival)
The history of the Cheetah People was relatively unknown to the Doctor. A more advanced civilisation that carved and built in stone originally existed. The people of this more advanced civilisation then began to domesticate the Kitlings in order to access their powers of remote viewing and teleportation but were themselves changed into the more primitive and animalistic society in return. Some were known to originally been from other species.
Around 1989, the Master found himself on the Cheetah World. He used the Cheetah People in an attempt to escape, sending them to Earth to capture humans, planning to allow them to partially convert, then use their teleportation to escape to Earth. The Master eventually escaped, but returned to the Cheetah World to fight the Seventh Doctor. Though the planet was destroyed, at least some of the Cheetah People appeared to survive on a new world, the Doctor remarking that the hunt went on. (TV: Survival)