In a century when environmental pollution is a major issue, polymers issued from bio-based monomers have gained important interest, as they are expected to be environment-friendly, and biocompatible, with non-toxic degradation products. In parallel, hyperbranched polymers have emerged as an easily accessible alternative to dendrimers with numerous potential applications. Glycerol (Gly) is a natural, low-cost, trifunctional monomer, with a production expected to grow significantly, and thus an excellent candidate for the synthesis of hyperbranched polyesters for pharmaceutical and biomedical applications. In the present article, we review the synthesis, properties, and applications of glycerol polyesters of aliphatic dicarboxylic acids (from succinic to sebacic acids) as well as the copolymers of glycerol or hyperbranched polyglycerol with poly(lactic acid) and poly(ε-caprolactone). Emphasis was given to summarize the synthetic procedures (monomer molar ratio, used catalysts, temperatures, etc.,) and their effect on the molecular weight, solubility, and thermal and mechanical properties of the prepared hyperbranched polymers. Their applications in pharmaceutical technology as drug carries and in biomedical applications focusing on regenerative medicine are highlighted.