olymer(s) [20,21], modifying the molecular structure via chain extension [19,22–24], cross-linking [25] and copolymerization [26], and adding special fillers [27–29], have been utilized to ameliorate the foamability of PBS. Besides, the crystallization and rheology properties of PBS as well as the solubility and diffusivity of the blowing agent in PBS, also significantly impact its foaming process [25].This paper provides a comprehensive review of the foaming mech- anism, fundamental performances, modification methods and foaming processing technologies for PBS and its foam applications. The foaming mechanisms of PBS are described, along with the effects of critical pa- rameters, such as crystallization and rheology of PBS, as well as solu- bility and diffusivity of blowing agent, on its foaming behaviors. We address the common modification methods of PBS for its foaming in recent years and compare the development of manufacturing technol- ogies used for PBS foams. This paper also explores the evolution of cell morphology in PBS foams, their potential applications and future chal- lenges. The structure diagram of this work is shown in Fig.