Poly(alkylene dicarboxylate)s constitute a family of biodegradable polymers with increasing interest for both commodity and speciality applications. Most of these polymers can be prepared from biobased diols and dicarboxylic acids such as 1,4-butanediol, succinic acid and carbohydrates. This review provides a current status report concerning synthesis, biodegradation and applications of a series of polymers that cover a wide range of properties, namely, materials from elastomeric to rigid characteristics that are suitable for applications such as hydrogels, soft tissue engineering, drug delivery systems and liquid crystals. Finally, the incorporation of aromatic units and alpha-amino acids is considered since stiffness of molecular chains and intermolecular interactions can be drastically changed. In fact, poly(ester amide)s derived from naturally occurring amino acids offer great possibilities as biodegradable materials for biomedical applications which are also extensively discussed.