Bioorthogonal click chemistry, first introduced in the early 2000s, has become one of the most widely used approaches for designing advanced biomaterials for applications in tissue engineering and regenerative medicine, due to the selectivity and biocompatibility of the associated reactants and reaction conditions. In this review, we present recent advances in utilizing bioorthogonal click chemistry for the development of three-dimensional, biocompatible scaffolds and cell-encapsulated biomaterials. Additionally, we highlight recent examples using these approaches for biomedical applications including drug delivery, imaging, and cell therapy and discuss their potential as next generation biomaterials.