Control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. In this talk, we shall establish analytical results on the existence and stability of steady states for a general class of pump-leak models. The key to these results is that pump-leak models possess a natural thermodynamic structure. We shall then use this thermodynamic structure as a guiding principle to obtain a spatial generalization of pump leak models - a PDE system that describes three-dimensional electrodiffusion and osmosis in cellular systems.