A colony ship was a type of spaceship operated by a species to carry colonists to another world for colonization purposes.
In 6012, a fusion-powered rocket acted as a colony ship bringing humans and the Hath to Messaline. Due to the war that broke out, the truth about the ship and the ship's terraforming device was forgotten and passed into legend with the colony ship becoming known as the Temple instead. After landing on the planet a week after the war began, the Tenth Doctor, Martha Jones, Donna Noble and Jenny discovered the temple and the truth about the war from the ship's logs. By revealing the truth and beginning the terraforming process, they were able to end the war and begin the intended colonization process. (TV: The Doctor's Daughter)
The Mondasians operated a colony ship that was hundreds of miles long and wide. However, it got stuck near a black hole and as a result experienced differing levels of time dilation. The ship was found by the Twelfth Doctor, Bill Potts, Nardole and Missy after responding to a distress call coming from the ship. The group became embroiled in battle with Cybermen created by the Master in the guise of Operation Exodus. Most of the Cybermen were destroyed by the Doctor, though the conflict forced him to regenerate while Nardole evacuated the surviving colonists to another floor for safety from the remaining Cybermen. The conflict also saw the forced regeneration of the Master and the apparently permanent demise of Missy. (TV: World Enough and Time, The Doctor Falls)