Injectable biodegradable copolymer hydrogels, which exhibit a sol–gel phase transition in response to external stimuli, such as temperature changes or both pH and temperature (pH/temperature) alterations, have found a number of uses in biomedical and pharmaceutical applications, such as drug delivery, cell growth, and tissue engineering. These hydrogels can be used in simple pharmaceutical formulations that can be prepared by mixing the hydrogel with drugs, proteins, or cells. Such formulations are administered in a straightforward manner, through site-specific control of release behavior, and the hydrogels are compatible with biological systems. This review will provide a summary of recent progress in biodegradable temperature-sensitive polymers including polyesters, polyphosphazenes, polypeptides, and chitosan, and pH/temperature-sensitive polymers such as sulfamethazine-, poly(β-amino ester)-, poly(amino urethane)-, and poly(amidoamine)-based polymers. The advantages of pH/temperature-sensitive polymers over simple temperature-sensitive polymers are also discussed. A perspective on the future of injectable biodegradable hydrogels is offered.