Degradable and bioresorbable aliphatic polyesters present great interest for biomedical and pharmaceutical applications. Among them, polylactide or poly(lactic acid) (PLA), polyglycolide or poly(glycolic acid) (PGA), and their copolymers are most attractive because of their outstanding biocompatibility, degradability, and versatility concerning physico-chemical and mechanical properties. This chapter aims to provide a comprehensive review on the state-of-the-art of PLA/PGA polymers, including the synthesis, properties, degradation, and applications. Efforts are focused on detailing the degradation mechanism and the effects of various factors such as PLA configuration, morphology, stereocomplexation, and chemical composition on the degradation behaviours. Hydrolytic degradation of large-size PLA/PGA polymers is characterised by autocatalysis of carboxyl end groups generated by ester bond cleavage. Faster internal degradation and degradation-induced morphological and compositional changes are three of the most important phenomena deduced from the behaviours of various polyesters. These findings should allow to predict the degradation of PLA/PGA polymers, which is of key importance for specific applications.