Cross shelf-break exchange is limited by the tendency of geostrophic flow to follow bathymetric contours, not cross them. However, small scale topography, such as canyons, can reduce the local lengthscale of the flow and increase the local Rossby number. These higher Rossby numbers mean the flow is no longer purely geostrophic and significant cross-isobath flow can occur. This cross-isobath flow includes both upwelling and downwelling due to wind-driven shelf currents and the strong cascading flows of dense shelf-water into the ocean. Tidal currents usually run primarily parallel to the shelf-break topography. Canyons cut across these flows and thus are often regions of generation of strong baroclinic tides and internal waves. Canyons can also focus internal waves. Both processes lead to greatly elevated levels of mixing. Thus, through both advection and mixing processes, canyons can enhance Deep Ocean Shelf Exchange. Here we review the state of the science describing the dynamics of the flows and suggest further areas of research, particularly into quantifying fluxes of nutrients and carbon as well as heat and salt through canyons.