A downhole actuator (30) comprises a tubular housing (34) which includes an indexing profile (42) on an inner surface thereof, and an indexing sleeve (46) mounted within the housing (34). The indexing sleeve (46) comprises an engaging arrangement including first and second axially spaced engagement members (52, 54) which cooperate with the indexing profile (42) of the housing (34) to be sequentially engaged by an actuation object (48) passing through a central bore (50) of the indexing sleeve (46) to drive the indexing sleeve (46) one discrete step of movement through the housing (34) towards an actuation site.