Biopolymer matrices reinforced with nanoparticles or nanofillers have received a great deal of attention over the past decades due to their various roles such as the augmentation of thermal, electrical, mechanical, and surface properties in tissue engineering, drug delivery, and implantation. Understanding the degradation kinetics of these polyesters is very important to successful applications of them. Hydrolysis is a widely agreed mechanism for the polyester degradation. According to this mechanism, hydrolytic degradation of these polyesters can be affected by the autocatalytic action of carboxyl groups as well as other factors such as hydrophilicity, crystallinity, and glass transition temperature. In this article, the effects of nanofillers on the autocatalytic action of carboxyl groups and the foregoing factors are examined. A particular attention is paid to carbon nanotubes (CNTs), which are a favorite candidate in a wide range of applications due to their unique thermal and electrical properties. Contradictory degradation results with CNTs are reported and analyzed. Finally, a future research perspective on these polyesters is discussed.