Hydrogels are crosslinked polymer networks that absorb substantial amounts of water. Cytoplasm and extracelleular matrix and connective tissues can be regarded as natural hydrogels. Synthetic hydrogels based on organic polymers have numerous applications, partly because they can mimic the mechanical, mass transport, and interfacial properties of biological tissues. Following a description of some of these applications, a brief survey will be provided of the ways hydrogels are synthesized and characterized, identifying important structural characteristics. A theory of free swelling of uncharged hydrogels due initially to Flory and Rehner will be reviewed. It will also be shown how the theory of Donnan equilibrium can be adapted to augment Flory-Rehner theory and model the free swelling of polyelectrolyte gels. Interesting and unexpected pattern formations, which occur when swelling is constrained, will also be discussed.