Narrow zones of intense shear deformation, i.e. viscous slip zones, are studied analytically with a one-dimensional time-dependent model of two half-spaces of identical or contrasting rheologies and ambient temperatures in relative motion. The rheologies of the half-spaces are strongly temperature-dependent and viscous heating maintains a thin zone of high temperature, low viscosity and large strain rate. The mathematical model is used to describe the structures of slip zones at ridge and plate-boundary transform faults, major continental strike—slip faults and at the top of subducting oceanic crust. No a priori assumption about slip-zone width or shear-stress magnitude is necessary; the thermal-mechanical structure of the slip zone evolves in time and all its characteristics are self-consistently determined. Slip-zone widths and shear stresses depend on the ambient temperatures, the relative velocity, the rheology and the length of time following the onset of relative motion; for reasonable geologic times, 0.1–10 M yr for example, slip zones are generally several kilometres wide and shear stresses are several hundred bars (tens of MPa). The region of intense shear in a viscous slip zone is an order of magnitude narrower than the width of the accompanying thermal anomaly. The maximum temperature generated by viscous dissipation in a slip zone depends only on the relative motion and the creep properties of the rocks; it is independent of slip-zone age and ambient temperature. Maximum temperatures associated with frictional heating are always less than those required for partial melting. The slip zone on a descending slab is influenced most strongly by the contrast in creep behaviour between the relatively soft oceanic crustal rocks and the hard, overlying mantle rocks; as a result, the slip zone is confined entirely within the oceanic crustal layer. Oceanic crustal rocks deform so readily that frictional heating in a slip zone on a descending slab cannot by itself lead to partial melting and thermal conduction from the hotter overriding mantle must play an essential role in heating the descending crust if melting is to occur therein. Because of the increase in the mantle temperature with depth, narrow slip zones in oceanic regions probably do not exist below depths of about 100 km; they may extend to greater depths beneath continents.