Polymers with the shape memory effect possess tremendous potential for application in diverse fields, including aerospace, textiles, robotics, and biomedicine, because of their mechanical properties (softness and flexibility) and chemical tunability. Biodegradable shape memory polymers (BSMPs) have unique benefits of long-term biocompatibility and formation of zero-waste byproducts as the final degradable products are resorbed or absorbed via metabolism or enzyme digestion processes. In addition to their application toward the prevention of biofilm formation or internal tissue damage caused by permanent implant materials and the subsequent need for secondary surgery, which causes secondary infections and complications, BSMPs have been highlighted for minimally invasive medical applications. The properties of BSMPs, including high tunability, thermomechanical properties, shape memory performance, and degradation rate, can be achieved by controlling the combination and content of the comonomer and crystallinity. In addition, the biodegradable chemistry and kinetics of BSMPs, which can be controlled by combining several biodegradable polymers with different hydrolysis chemistry products, such as anhydrides, esters, and carbonates, strongly affect the hydrolytic activity and erosion property. A wide range of applications including self-expending stents, wound closure, drug release systems, and tissue repair, suggests that the BSMPs can be applied as actuators on the basis of their shape recovery and degradation ability.