New technologies for the conversion of biomass into high-value chemicals, including polymers and plastics, is a must and a challenge. The development of green processes in the last decade involved a continuous increase of the interest towards the synthesis of polymers using in vitro biocatalysis. Among the remarkable diversity of new bio-based polymeric products meeting the criteria of sustainability, biocompatibility, and eco-friendliness, a wide range of polyesters with shorter chain length were obtained and characterized, targeting biomedical and cosmetic applications. In this review, selected examples of such specialty polymers are presented, highlighting the recent developments concerning the use of lipases, mostly in immobilized form, for the green synthesis of e-caprolactone co-polymers, polyesters with itaconate or furan units, estolides, and polyesteramides. The significant process parameters influencing the average molecular weights and other characteristics are discussed, revealing the advantages and limitations of biocatalytic processes for the synthesis of these bio-based polymers.