Krillitanes were a race of mutating aliens seen in the episode School Reunion. They could take physical features from races they conquered. For example, when the Doctor first met them they were humanoids with long necks. By the time of School Reunion they had a completely different form. The following information is only valid for the Krillitane shown in School Reunion.
The Krillitanes are large, bat-like humanoids (they had taken the wings from the inhabitant of Bessan). They had red-grey skin, sharp claws and a flattened, fanged face. They sleep upside down like bats and have a very good sense of hearing. As well a the bat-form, the Krillitanes can create a illusion of a human (which Mr Finch preferred). Krillitanes are carnivorous and will eat other sentient creatures. They also produced Krillitane oil which can increase intelligence in humans but is currently deadly for Krillitanes. They are aware of the Time Lords and their extinction.
During the events of School Reunion, they had taken over Deffry Vale School. Using the Krillitane oil and an advanced computer network, they were using the brains and imagination of the students as a type of computer in order to work out the Skasis Paradigm.