Aliphatic polycarbonates have gained increased attention as biomaterials largely owing to their biocompatibility and tunable degradation. Moreover, the ability to introduce functional handles in the polymer backbone through careful design of cyclic carbonate monomers or copolymerization with other biodegradable polymers has significantly contributed to the interest in exploiting this class of materials for biomedical applications. Such investigations have enabled their utility to be expanded to a wide variety of applications in the biomedical field, from drug delivery to tissue regeneration and the design of vascular grafts. Herein, we review the synthesis, degradation, and studies into biomedical applications of aliphatic polycarbonates obtained by ring-opening polymerization of cyclic carbonate monomers (ring sizes between 6 and 8). While all synthetic methods will be covered, particular emphasis will be given to materials that have been exploited for therapeutic applications in vitro and in vivo.