An overview is given of new ferromagnetic Heusler alloys like Ni-Co-(Al, Ga, Zn), Co-Ni-(Al, Ga, Zn), Fe-Ni-(Al, Ga, Zn) and Fe-Co-(Al, Ga, Zn), which are compared with today's mostly investigated systems such as Ni-Mn-Z (Z = Al, Ga, In, Sn, Sb). The investigations are based on first-principles as well as Monte Carlo calculations. For some new systems, the simulations of atomic structure and magnetic and electronic properties allow to predict higher Curie and martensitic transformation temperatures than those of prototypical Ni-Mn-Z materials. Some of the new materials may be distinguished for devices which exploit the magnetic shape memory effect. Interestingly, in general, all off-stoichiometric alloys display competing antiferromagnetic correlations, which may be important for devices using the magnetocaloric effect. The Curie temperatures are obtained from Monte Carlo simulations using magnetic exchange parameters from ab initio calculations while the structural instability is inferred from local minima in the ab initio total energy curves as a function of the tetragonal distortion. The manifestation of phonon softening as a precursor of structural transformations is present in the austenitic phase of most of the calculated ferromagnetic shape-memory alloys. However, quite remarkably, we find that phonon softening is absent in a few systems such as Co2NiGa.