Nanoparticles are the cornerstone of nanotechnology. Their crystal structure and relation to shape are still open problems despite a lot of advances in the field. The classical theory of nanoparticle stability predicts that for sizes <1.5-2 nm the icosahedral structure should be the most stable, then between around 2-5 nm, the decahedral shape should be the most stable. Beyond that, face-centered-cubic (FCC) structures will be the predominant phase. However, in the experimental side, icosahedral (I(h)) and decahedral (D(h)) particles can be observed much beyond the 5 nm limit. In fact, it is possible to find I(h) and D(h) particles even in the mesoscopic range. Conversely, it is possible to find FCC particles with a size <1.5 nm. In this paper we review a number of the mechanisms proposed in the literature that allow the stabilization of nanoparticles. Some of the mechanisms are very interrelated and it becomes difficult to distinguish between them.