Degradable aliphatic poly(trimethylene carbonate) (PTMC) and poly(carbonate-co-esters) of trimethylene carbonate (TMC) with lactides, glycolide, and ε-carprolactone present great interest for applications in the fields of surgery, tissue repair and regeneration, tissue engineering, and sustained drug delivery. This chapter aims to provide a comprehensive review on the state-of-the-art of the synthesis mechanisms, structure–properties, degradation behaviours, and biomedical applications of TMC-based polymers. The ring-opening polymerisation mechanisms are discussed in detail, including anionic, cationic, coordination, and enzyme-catalysed polymerisation. The in vitro and in vivo degradation of PTMC and copolymers are described. PTMC homopolymer can be degraded in vivo or in the presence of enzymes. Degradation of copoly(carbonate-esters) is similar to that of aliphatic polyesters involving water uptake, molar mass decrease, weight loss, and morphological and compositional changes. Understanding of the degradation characteristics is of key importance for the development of medical and pharmaceutical applications.