Hydrogels, due to their unique biocompatibility, flexible methods of synthesis, range of constituents, and desirable physical characteristics, have been the material of choice for many applications in regenerative medicine. They can serve as scaffolds that provide structural integrity to tissue constructs, control drug and protein delivery to tissues and cultures, and serve as adhesives or barriers between tissues and material surfaces. In this work, the properties of hydrogels that are important for tissue engineering applications and the inherent material design constraints and challenges are discussed. Recent research involving several different hydrogels polymerized from a variety of synthetic and natural monomers using typical and novel synthetic methods are highlighted. Finally, special attention is given to the microfabrication techniques that are currently resulting in important advances in the field.