An imp was a mythical creature. It was depicted as a small demonic-looking humanoid.
Several species encountered by the Doctor resembled imps. These included the Drachee (AUDIO: The Brood of Erys) and the Tregannan (AUDIO: The Spectre of Lanyon Moor) Flux imps from Pherkad array had horns and hooves. (AUDIO: The Witch from the Well) The Vvormak could create psychic projections which looked like imps. (PROSE: The Shadow in the Glass)
While in the Infernal Regions, Jason Kane met an imp that put him in contact with Agragazar Fletchcock. (PROSE: The Door into Bedlam)
Before Emile Mars-Smith died, he made a demonic pact with an imp. (PROSE: Where Angels Fear)
Other references
After the Eleventh Doctor's conflict at the Pandorica, (TV: The Pandorica Opens) he gained the title, "Imp of the Pandorica." (TV: Twice Upon a Time)