Poly (butylene succi- nate) (PBS), an aliphatic polyester polymerized from 1,4-butanediol and succinic acid, can be obtained from renewable resources that are bio-based and biodegradable. PBS foams with various cellular structures display good heat insulation, excellent toughness, and well biocompatibility, making them suitable for applications such as packaging and adsorption materials. However, the low melt viscoelasticity and melt strength of PBS hinder its foaming process without modification. This review provides an overview of commonly used modification methods and their effects on the rheological, thermal and foaming properties of PBS, as well as the solubility and diffusivity of blowing agents in PBS. Subsequently, the principles of foaming processing conditions, foaming methods, blowing agent types, cell morphology evolution and potential applications of PBS foams are described. Finally, the current challenges and potential solutions for PBS foaming and its applications are discussed in detail.