A variable geometry turbine of the kind used in a turbocharger has a variable geometry element such as a nozzle ring that is operated by an actuator. The actuator comprises a motor which drives a cross-shaft in rotation. The cross-shaft in turn drives a pair of guide rods on which the nozzle ring is supported in translation so as to move the nozzle ring and control the width of the inlet passage of the turbine. The cross-shaft and guide rods are drivingly engaged by a rack and pinion or thread or another toothed or threaded formation suitable for converting rotational movement into translational movement. The cross-shaft can be located in close proximity to the guide rods and the output of the motor shaft so as to provide a compact package. Moreover, the torque required to resist movement of the nozzle ring in operation is much reduced in comparison to existing designs.