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NiMnGa based ferromagnetic alloys are ideal candidates for applications such as actuators, magnetic refrigerators or magnetostrictive transducers due to their attractive properties such as magnetic field induced shape memory effect and large magnetocaloric effect. The properties of these alloys (e.g., the martensitic transformation temperature T) sensitively depend on the composition. Understanding the composition dependence of these properties so as to design the alloy as desired is one of the main research topics in this area. In recent years, we have investigated the composition dependent elastic modulus and phase stability of NiMnGa-based alloys by using a first-principles method, in hope of clarifying their connection to the properties of these alloys. In this article, we review the main results of our investigations. We show that the tetragonal shear modulus C′ is a better predictor of the composition dependent T than the number of valence electrons per atom ( e/ a) since the general T∼ C′ correlation works for some of the alloys for which the T∼ e/ a correlation fails, although there exist several cases for which both the general T∼ C′ and T∼ e/ a correlations break down. Employing the experimentally determined modulation function, the complex 5-layer modulated (5M) structure of the martensite of NiMnGa and the Al-doping effect on it are studied. We find that the shuffle and shear of the 5M structure are linearly coupled. The relative stability of the austenite and the martensites is examined by comparing their total energies. The non-modulated martensite β″′ with the tetragonality of the unit cell c/ a>1 is shown to be globally stable whereas the 5M martensite with c/ a<1 is metastable. The critical Al atomic fraction over which the martensitic transformation between the 5M martensite and austenite cannot occur is predicted to be 0.26, in reasonable agreement with experimental findings. [ABSTRACT FROM AUTHOR]