Among degradable and biodegradable polymers, aliphatic polyesters are the most attractive compounds for biomedical and pharmaceutical applications. Polymers and copolymers derived from lactic acid enantiomers and/or glycolic acid have been extensively investigated because of their outstanding biocompatibility, bioresorbability, and versatility. Attention has also been paid to poly(e-caprolactone). The potential of these polymers to serve as matrices for sustained drug delivery has been prospected during the past two decades. However, literature is still full of confusing statements and controversial data. This chapter is aimed at introducing the state-of-the-art in this field from the present understanding of the synthesis and degradation mechanisms of these polymers. Discussion is focused on the effects of various factors on matrix degradation and drug release characteristics, namely polymer morphology, chemical composition and configurational structure, molar mass and molar mass distribution, size and porosity, drug/matrix interaction, g irradiation, pH and ionic strength, in vitro or in vivo media. Indications are given in order to help the readers in taking advantages of all the underlined particularities from a practical viewpoint.