The giant magnetically-induced deformation of ferromagnetic shape memory alloys results from the magnetic field-induced rearrangement of twinned martensite under the magnetic field. This deformation is conventionally referred to as the magnetic-field-induced-strain (MFIS). The MFIS is comparable in value with the spontaneous deformation of crystal lattice during the martensitic transformation of an alloy. Although the first observations of MFIS were reported more than 30 years ago, it has got a world-wide interest 20 years later after the creation of the Ni–Mn–Ga alloy system with its practically important room-temperature martensitic structure and experimental evidence of the large magnetostriction. The underlying physics as well as necessary and sufficient conditions for the observation of MFIS are the main focus of this chapter. A magnetostrictive mechanism of the unusual magnetic and magnetomechanical effects observed in Ni–Mn–Ga alloys is substantiated and a framework of consistent theory of these effects is outlined starting from the fundamental conception of magnetoelasticity and the commonly known principles of ferromagnetism and linear elasticity theories. A reasonable agreement between the theoretical deductions and available experimental data is demonstrated and, in this way, a key role of magnetoelastic coupling in the magnetomechanical behavior of Ni–Mn–Ga alloys is proved. A correspondence of magnetostrictive mechanism to the crystallographic features of MFIS and the basic relationships of the thermodynamics of solids are discussed.