Polyester elastomers are soft, biodegradable and biocompatible and are commonly used in various biomedical applications, especially in tissue engineering. These synthetic polyesters can be easily fabricated using various techniques such as solvent casting, particle leaching, molding, electrospinning, 3-dimensional printing, photolithography, microablation etc. A large proportion of tissue engineering research efforts have focused on the use of allografts, decellularized animal scaffolds or other biological materials as scaffolds, but they face the major concern of triggering immunological responses from the host, on top of other issues. This review paper will introduce the recent developments in elastomeric polyesters, their synthesis and fabrication techniques, as well as their application in the biomedical field, focusing primarily on tissue engineering in ophthalmology, cardiac and vascular systems. Some of the commercial and near-commercial polyesters used in these tissue engineering fields will also be described.