Degradable aliphatic polyesters deriving from lactides, glycolide and e-caprolactone present great interest for applications in the fields of surgery, tissue repair and regeneration, and sustained drug delivery. The hydrolytic degradation of aliphatic polyesters is a complex process involving many physico-chemical phenomena, namely water uptake, ester bond cleavage, neutralization of carboxyl endgroups at the surface, autocatalysis inside, crystallization, and diffusion and solubilization of soluble oligomers. These phenomena can be monitored by using various in vitro physicochemical test methods including visual examination, environmental scanning electron microscope (ESEM), proton nuclear magnetic resonance (1H NMR), size-exclusion chromatography (SEC), X-ray diffraction (XRD), differential scanning calorimetry (DSC), electron spray injection mass spectrometry (ESI-MS), capillary zone electrophoresis (CZE), weight loss, mechanical properties, etc. Factors such as polymer morphology, chemical composition and configurational structures, MW and MW distribution, size and porosity, chemically reactive additives, can strongly affect the degradation of polymers. This paper aims to present the state-of-the-art on the basis of recent advances in this domain.