In the shape memory alloys (SMAs) the thermal triggering induces reversible dimensional change by the phase transformation – these materials may also be ferrior ferromagnetic, however, here only the ferromagnetic SMAs are discussed. In certain SMAs the austenitemartensite phase transformation is influenced by the magnetic field as either austenite or martensite is promoted by the field and this is exploited for the dimensional changes. However, in the magnetic shape memory (MSM) alloys no phase transformation occurs as the remarkable dimensional changes take place by the twin variant changes in the martensitic phase activated by the external magnetic field at constant temperature. In addition to the phase transformation or magnetic shape memory effect, the applied magnetic field may also result in the conventional magnetostriction (MS), enhance the superelasticity (magneticfieldassisted superelasticity MFAS) or induce the giant magnetocaloric effect (GMCE). Certain alloys such as NiMnGa may even be multifunctional showing more than one of these effects. The present paper gives an overview of the different types of the magnetically activated SMA alloys, their properties as well as their potentials for applications in the frameworks of the recent studies.