A compressor comprises a housing having an axial intake and an annular outlet volute. An impeller is mounted on a shaft for rotation about a shaft axis between the axial intake and the annular outlet volute. The impeller has a plurality of blades, each blade having a front edge facing the axial intake and a tip. The annular outlet volute includes an annular diffuser passage surrounding the impeller. The annular diffuser passage has a diffuser inlet downstream of the plurality of blades and a diffuser outlet communicating with the annular outlet volute, the tips of the blades sweeping across said diffuser inlet during use. A wall of the housing which defines the annular diffuser passage and which extends over the front edges of the blades defines an annular recess extending from the diffuser inlet towards the diffuser outlet.