Artificially engineered proteins and synthetic polypeptides have attracted widespread interest as building blocks for polymer hydrogels. The biophysical properties of the proteins, such as molecular recognition abilities, folded chain structures, and sequence-dependent thermodynamic behavior, enable advances in functional, responsive, and tunable gels. This review discusses the design of polymer hydrogels that incorporate protein domains, highlighting new challenges in polymer physics that are presented by this emerging class of materials. Five types of engineered protein hydrogels are discussed: (a) physically associating protein polymer gels, (b) amorphous artificially engineered protein networks, (c) engineered proteins with crystalline domains, (d) stretchable protein tertiary structures in gels, and (e) protein gels with biological recognition properties. The physics of the protein component and the physical properties of the resulting hydrogels are summarized, illustrating how advances in understanding these systems are leading to exciting novel biofunctional hydrogels.