Biomaterials have been extensively used to leverage beneficial outcomes in various therapeutic applications, such as providing spatial and temporal control over the release of therapeutic agents in drug delivery as well as engineering functional tissues and promoting the healing process in tissue engineering and regenerative medicine. This perspective presents important milestones in the development of polymeric biomaterials with defined structures and properties. Contemporary studies of biomaterial design have been reviewed with focus on constructing materials with controlled structure, dynamic functionality, and biological complexity. Examples of these polymeric biomaterials enabled by advanced synthetic methodologies, dynamic chemistry/assembly strategies, and modulated cell-material interactions have been highlighted. As the field of polymeric biomaterials continues to evolve with increased sophistication, current challenges and future directions for the design and translation of these materials are also summarized.