A variable geometry turbine comprises a housing defining a chamber within which a turbine wheel is mounted. The chamber has an annular inlet having a width defined between side walls of the housing. An array of vanes is mounted within the inlet, each vane having a length extending across the inlet, and a chordal length defined between leading and trailing vane edges. The vanes can be pivoted to adjust the effective cross-section area of the annular inlet. Each vane is pivotable between a first position in which the area of the inlet is a minimum and a second position in which the area of the inlet is a maximum. At least one of the side walls is configured so that clearance between the side wall and at least a portion of the adjacent chordal edge of each vane varies in a predetermined manner as the vane moves.