The syntheses, properties and selected applications of star-shaped polymers with arms composed of homo- or copolymers of polylactide (PLA) is reviewed. The star-shaped (including miktoarm stars), dendritic, and branched polymers with a specified or varying numbers of arms were synthesized depending on the applied core molecule. Examples of a large number of various structures of star-shaped PLA polymers are precisely described. The growing interest in the synthesis of star-shaped and branched PLAs is primarily motivated by their potential applications in the biomedical and pharmaceutical areas. Therefore, the thermal, rheological, and mechanical properties, as well as various applications, of PLA stars as, for example, drug carriers, medical materials, and components of hydrogels, are also reported. (C) 2018 Elsevier B.V. All rights reserved.