The vast majority of shock wave–boundary-layer interactions in practical applications like supersonic aircraft intakes are three dimensional in nature. The complex behaviour of such interactions can generally be understood by combining the flow physics of a limited number of canonical cases. The physical understanding of these flow fields developed by numerous investigators over the last half century is reviewed, focusing predominantly on steady aspects of turbulent, uncontrolled interactions in the transonic and supersonic regimes, i.e. for Mach number less than 5. Key physical features of the flow fields and recent developments are described for swept compression corners, various fin interactions, semi-cones, vertical cylinder- induced interactions, swept oblique shock reflections and flared cylinders. In addition to the canonical geometries, a different type of three dimensionality concerning sidewall effects in duct flows, like intakes or propulsion systems, is also reviewed. The underlying mechanisms, centred on pressure waves propagating from the corner regions, are introduced and the implications for separation unsteadiness and flow control are discussed.