When elastomers were first proposed as useful materials for regenerative medicine a few decades ago, their high versatility and suitability for a diverse and wide range of in vivo applications could not have been predicted. Due to their ability to recover after deformation, these materials were first introduced in tissue engineering in an attempt to mimic the mechanical properties of the extracellular matrix. Furthermore, elastomeric characteristics have been described as important criteria for cell interaction by modulating cellular behavior. From soft to hard tissues, elastomers have demonstrated degradation, mechanical, and biocompatibility requirements in accordance with the target tissue. In this feature article, biodegradable synthetic polyester elastomers that have been reported in the literature are discussed, with special focus on those that show promise for in vivo tissue replacement. Their satisfactory performance in vivo shows the promise of elastomers for use in regenerative medicine. However, further investigation is required to demonstrate the prospect of elastomer-based therapies in clinical trials.