A compressor includes a housing, a compression mechanism, an input shaft rotatable on an axis thereof, an output shaft for driving the compression mechanism, a transmission for transmitting torque from the input shaft to the output shaft and also changing the rotating speed of the input shaft and a control device for controlling the operation of the transmission. The transmission includes a plurality of planetary rollers, a carrier rotatably supporting the respective planetary rollers and being integrally rotatable with the input shaft, a sun roller engaged with the respective planetary rollers and integrally rotatable with the output shaft and a ring roller engaged with the respective planetary rollers. The ring roller can be fixed to the housing or rotatable relative to the housing. The control device includes a one-way clutch allowing the ring roller to rotate only one direction relative to the carrier and a clutch fixing the ring roller to the housing or allowing the ring roller to rotate relative to the housing. The input shaft, the carrier, the respective planetary rollers and the sun roller cooperate to form an assembly that can move as a unit relative to the housing in the direction that is parallel to the axis.