Biobased polymers have seen their attractiveness increase in recent decades thanks to the significant development of biorefineries to allow access to a wide variety of biobased building blocks. Polyesters are one of the best examples of the development of biobased polymers because most of them now have their monomers produced from renewable resources and are biodegradable. Currently, these polyesters are mainly produced by using traditional chemical catalysts and harsh conditions, but recently greener pathways with nontoxic enzymes as biocatalysts and mild conditions have shown great potential. Bacterial polyesters, such as poly(hydroxyalkanoate)s (PHA), are the best example of the biotic production of high molar mass polymers. PHAs display a wide variety of macromolecular architectures, which allow a large range of applications. The present contribution aims to provide an overview of recent progress in studies on biobased polyesters, especially those made from short building blocks, synthesized through step-growth polymerization. In addition, some important technical aspects of their syntheses through biotic or abiotic pathways have been detailed.