Aliphatic polyesters presently constitute the most attractive class of artificial polymers which can degrade in contact with living tissues or under outdoor conditions. Work has been in progress for the last two decades which has led to applications in surgery and in pharmacology. Basically, these compounds are also of interest for outddor applications such as packaging material or mulch films and in plant therapy by controlled delivery of pesticides or insecticides in agriculture, although they are still too expensive. Factors which can affect their biodegradation have been investigated world-wide. However, the literature contains confusing statements and controversial data. This chapter is aimed at clarifying the state-of-the-art. After general considerations, including comments on terminology and on enzymatic and/or hydrolytic degradation mechanisms, discussion is focused on the effects of influencing factors, in particular the main structural parameters. Although poly(a-hydroxyacids) derived from lactic and glycolic acids are, by far, the most important members of the aliphatic polyester family, poly(b-hydroxyacids) and other aliphatic polyesters such as poly(e-caprolactone), polydioxanones, etc. are also considered.