The ever-increasing use of polymers in commodities due to their ease of processing and low price, has arisen as one of the current concerns for society. The non-biodegradability of many of the conventional polymers, like polyethylene and polypropylene, have led to serious ecological problems. In contrast, biodegradable polymers (BPs) are naturally recycled, because they can be degraded by the enzymatic action of microorganisms and by abiotic processes. Degradable polymers are sustainable, recyclable, and environmentally friendly plastic materials, which are considered an alternative to traditional polymers. Among them, biodegradable polyesters such as poly(lactic acid) (PLA), poly(glycolic acid) (PGA), polycaprolactone (PCL), poly(hydroxyalkanoates) (PHA) have emerged as examples of technical and economical alternatives that are able to substitute traditional polymers in order to improve the biodegradability of these kind of materials. In this context, this work aims to emphasize the importance of BPs as promoters of environmental responsibility and searching for new and improved disposable materials and biomaterials. The main synthetic routes used for the development of these polymers and the different degradation mechanism described for them are summarized, in addition to their main applications.