Nowadays, ferromagnetic shape memory Heusler alloys are ones of famous multifunctional materials exhibiting many interesting features in the temperature interval of the martensitic transformation due to the strong interrelation between crystal structure and magnetic order. The multiferroic, magnetoresistive, martensitic and related magnetic shape-memory behavior as well as magnetocaloric properties are examples of these unique features. Generally, tuning of both structural and magnetic transition temperatures can be useful to achieve better functional properties. Today, the optimization problem of Heusler compounds is of a great importance. In this chapter, we review the most important features of ternary and quaternary ferromagnetic shape memory Ni-Mn-In and Ni-Mn-In-Z materials, which are experimentally and theoretically obtained in the last three years. We discuss the experiments devoted to the study of phase diagrams, thermomagnetizations, magnetic field and stress induced strains, magnetoresistance and magnetocaloric effects. The theoretical investigations of magnetic and structural properties are reviewed in the framework of the phenomenological approach, first-principles and Monte Carlo methods.