Porous shape memory polymers (SMPs) exhibit geometric and volumetric shape change when actuated by an external stimulus and can be fabricated as foams, scaffolds, meshes, and other polymeric substrates that possess porous three-dimensional macrostructures. These materials have applications in multiple industries such as textiles, biomedical devices, tissue engineering, and aerospace. This review article examines recent developments in porous SMPs, with a focus on fabrication methods, methods of characterization, modes of actuation, and applications.