A review is presented of some recent studies relating to the solution of Richards` equation for the description of water infiltration in unsaturated soils. Following a brief summary of the relevant theory, boundary conditions of both the Dirichlet type (constant concentration) and the Neumann type (constant flux) are outlined. Quasi-analytical and analytical solutions are then discussed and the significance of recent constant-flux analytical solutions described. Some of the relevant computer-based numerical studies are considered, with this being followed by work relating to algebraic expressions for the prediction of the surface water content and the time to ponding during a constant-flux infiltration regime.