Microstructural features determine many of the macroscopic properties of NiTi shape memory alloys (for instance, strength, ductility, transformation temperatures, fatigue and fracture behavior). But many of these properties are also closely related to more fundamental physical processes that are directly determined by the properties and electronic structure of the crystal lattice. To obtain a solid understanding, and to allow for optimization of microstructures in terms of materials engineering, one would ideally like to study these more fundamental physical parameters. However, in NiTi, the relevant processes on the atomistic scale are rarely directly accessible by experimental methods. Fortunately, theoretical approaches (i.e., quantum-mechanical first-principles calculations) allow catching a glimpse of some interesting atomistic aspects of shape memory alloys. In this contribution, recent results from such ab initio simulations are reviewed. Special attention is devoted to the mechanical properties and relative stability of the different phases of NiTi and of Ni-rich particles. Moreover, several consequences of the novel results (in particular, high stiffness of B19' martensite on the atomistic scale), their agreement with recent experiments, and their use for micromechanical and continuum mechanical models are discussed. The importance of inelastic, but reversible deformation mechanisms, is highlighted. Finally, current limitations of the method, as well as its relevance for science and engineering, are addressed. Future challenges for ab initio simulations, such as an analysis of twinned structures, finite temperature simulations, or investigations of alloying effects on the transformation behavior, are pointed out.