Sub-inertial disturbances confined over stratified continental shelves are generally described as coastal trapped waves (CTWs). Most theoretical discussions of CTWs are based on the assumption that the coast and shelf profile are uniform in the longshore direction. However in practice there may be significant longshore variations in shelf depth profiles and coastline curvature. These longshore variations can give rise to regions of localised wave propagation with modes decaying outside these regions in both the longshore and offshore directions. This talk discusses evidence for the existence of these localised CTWs on ocean shelves and in large lakes and presents analytical and numerical models for both barotropic and baroclinic flows that show that topographic effects can be classified into boundary, steepness and curvature effects. It is shown that sufficiently strong stratification prevents trapping but can introduce other singularities.