Insufficient spatial or temporal resolution is a common source of errors in numerical solutions for both water flow and solute transport in the variably unsaturated vadose zone. Evaporation near the surface, as well as infiltration into initially dry soil profiles, typically create mobile local regions with large gradients of the pressure head. Convection-dominant transport of solutes during water flow in soil also tends to create steep moving fronts of concentration with large localized concentration gradients. Groundwater flow and solute transport in highly heterogeneous aquifers similarly tend to be preferentially channeled through regions of high flow rates. Without due consideration of special resolution requirements for such critical cases of flow and transport, simulations using traditional finite difference (FDM) and finite element (FEM) numerical methods typically provide inaccurate solutions characterized by undesirable features such as oscillation and numerical dispersion. Incorporation of local adaptive grid refinement (LAGR) algorithms in numerical models for solving such cases is an effective approach that has been used to provide accurate numerical approximations by automated adjustment of local spatial resolution. Local error estimates are typically utilized to optimize spatial resolution. Definite advantages, as well as some limitations, exist for using LAGR algorithms in FDM and FEM numerical models for flow and transport in soils.