bPolyhydroxyalkanoates (PHAs) are storage compounds synthesized by numerous microorganisms and have attracted the interest of industry since they are biobased and biodegradable alternatives to fossil fuel-derived plastics. Among PHAs, poly(3-hydroxypropionate) [poly(3HP)] has outstanding material characteristics and exhibits a large variety of applications. As it is not brittle like, e.g., the best-studied PHA, poly(3-hydroxybutyrate) [poly(3HB)], it can be used as a plasticizer in blends to improve their properties. Furthermore, 3-hydroxypropionic acid (3HP) is considered likely to become one of the new industrial building blocks, and it can be obtained from poly(3HP) by simple hydrolysis. Unfortunately, no natural organism is known to accumulate poly(3HP) so far. Thus, several efforts have been made to engineer genetically modified organisms capable of synthesizing the homopolymer or copolymers containing 3HP. In this review, the achievements made so far in efforts to obtain biomass which has accumulated poly(3HP) or 3HP-containing copolymers, as well as the properties of these polyesters and their applications, are compiled and evaluated.