Uptake of water by plant roots can be considered at two different Darcian scales, referred to as the mesoscopic and macroscopic scales. At the mesoscopic scale, uptake of water is represented by a flux at the soil-root interface, while at the macroscopic scale it is represented by a sink term in the volumetric mass balance. At the mesoscopic scale, uptake of water by individual plant roots can be described by a diffusion equation, describing the flow of water from soil to plant root, and appropriate initial and boundary conditions. The model involves at least two characteristic lengths describing the root-soil geometry and two characteristic times, one describing the capillary flow of water from soil to plant roots and another the ratio of supply of water in the soil and uptake by plant roots. Generally, at a certain critical time, uptake will switch from demand-driven to supply-dependent. In this paper, the solutions of some of the resulting mesoscopic linear and nonlinear problems are reviewed. The resulting expressions for the evolution of the average water content can be used as a basis for upscaling from the mesoscopic to the macroscopic scale. It will be seen that demand-driven and supply-dependent uptake also emerge at the macroscopic scale. Information about root systems needed to operationalize macroscopic models will be reviewed briefly.