Polymers with ester linkages in their main chain comprise a family of polymers with immense diversity and versatility. This review deals with the preparation of such polymers from dicarboxylic acid monomers, and the result in terms of properties and applicability. Polyesters alone, and their copolymers with amides, anhydrides, urethanes, imides, ethers or other functional groups, offer countless opportunities to tune the properties of the resulting material within a broad range. Of particular interest is the inherent biodegradability of the ester linkage. Biodegradability is sought after in a wide range of applications, above all in the preparation of environmentally friendly polymers and biomedical materials for temporary surgical use and in drug delivery.