Porous shape memory polymers (SMPs) include foams, scaffolds, meshes, and other polymeric substrates that possess porous three-dimensional macrostructures. Porous SMPs exhibit active structural and volumetric transformations and have driven investigations in fields ranging from biomedical engineering to aerospace engineering to the clothing industry. The present review article examines recent developments in porous SMPs, with focus given to structural and chemical classification, methods of characterization, and applications. We conclude that the current body of literature presents porous SMPs as highly interesting smart materials with potential for industrial use.