The Doctor discovered (in "Dalek", "Bad Wolf"/"The Parting of the Ways" & "Doomsday") that some Daleks had survived. He also eventually learned (in "Utopia") that the Master had fled the Time War & had used a chameleon arch to hide himself as the human Professor Yana. Until "The Day of the Doctor", however, these & the Doctor himself were the only known survivors of the 2 principal combatant species.
In "The Day of the Doctor", we learned that Gallifrey was not actually destroyed, but frozen in a pocket universe, meaning that a large number of Time Lords also survived. (We don't know just how many, though.)