We review viscoplastic flow over inclined surfaces, focusing on constant-flux extrusions from small vents and the slumping of a fixed volume of material. Lubrication theory is used for shallow and slow flows to reduce the governing equations to a nonlinear diffusion-type equation for the local fluid depth; this model is used as the basis for exploration of the problem. Theory is compared to experiments. A number of complications and additional physical effects are discussed that enrich real situations. (c) 2006 Elsevier B.V. All rights reserved.