The thermally induced shape memory effect (SME) is the capability of a material to fix a temporary (deformed) shape and recover a 'memorized' permanent shape in response to heat. SMEs in polymers have enabled a variety of applications including deployable space structures, biomedical devices, adaptive optical devices, smart dry adhesives and fasteners. By the incorporation of magnetic nanoparticles (mNP) into shape-memory polymer (SMP), a magnetically controlled SME has been realized. Magnetic actuation of nanocomposites enables remotely controlled devices based on SMP, which might be useful in medical technology, e.g. remotely controlled catheters or drug delivery systems. Here, an overview of the recent advances in the field of magnetic actuation of SMP is presented. Special emphasis is given on the magnetically controlled recovery of SMP with one switching temperature T(sw) (dual-shape effect) or with two T(sw)s (triple-shape effect). The use of magnetic field to change the apparent switching temperature (T(sw,app)) of the dual or triple-shape nanocomposites is described. Finally, the capability of magnetic nanocomposites to remember the magnetic field strength (H) initially used to deform the sample (magnetic-memory effect) is addressed. The distinguished advantages of magnetic heating over conventional heating methods make these multifunctional nanocomposites attractive candidates for in vivo applications.