Recent developments in synthesis techniques have enabled production of colloidal nanoparticles of with intricate shapes with unprecedented precision. When put under high osmotic pressure, faceted particles can self-assemble into intricate structures that find applications in photonic and photoelectric systems. Thus, it is of engineering interest to understand design principles governing nanoparticle self-assembly. Not only can such understanding be of practical importance, but it can also reveal general principles about the way how naturally occurring systems self-assemble into complex nanostructures. In this thesis, I will discuss findings from our Monte Carlo simulations that reveal the influence of the shape of a nanoparticle on its self-assembly. We find that the way such nanoparticles are faceted has important consequences upon how quickly they self-assemble, providing us ‘design rules’ for the nanoparticle shape. For example, octahedral particles tend to align their facets in the disordered phase, but not in the ordered phase. Entropic preference to facet alignment in the disordered phase results in a large kinetic barrier for its disorder-order transition. In our studies of a variety of shapes (such as cubes, truncated cubes and gyrobifastigia), we have found transitions that show departures from classical nucleation that motivate development of new theories and simulation methods. Based on the geometric properties of the particle shape, such particles may also form mesophases – phases that have an intermediate degree of order between disordered and ordered phases. I will also illustrate examples of transitions to and from mesophases – and how their existence might hinder or accelerate disorder to order transitions. We studied how either a rotator mesophase or a liquid crystal forms a crystal; the former case illustrates a transition primarily involving particle reorientations with minimal translations, while the latter is an example of a transition with large particle translations with minimal reorientations. In both cases, we the structure and formation kinetics of the incipient crystalline nucleus could depart from the classical theory considerably. These results contribute to improving our current understanding of self-assembly of nanoparticles, with predictions that are suitable for experimental validation in near future.