A variety of self-assembled nanostructures can be grown from either group IV or III-V semiconductors, including nanowires, quantum dots, and more complex structures. In many ways, the behavior of different semiconductors is surprisingly similar. However, the growth of III-V nanostructures has an additional degree of freedom, the III/V ratio; and in important respects III-V growth can be very different than group IV. This talk will present recent results for two widely-studied III-V systems: nanowire growth, and droplet epitaxy. In each case, theoretical modeling explains some surprising results of recent experiments. Using in-situ microscopy to study growth of GaP nanowires, Chou, Ross et al. have found remarkable differences in kinetics depending on III/V ratio. In particular, the presence of crystal defects causes dramatic fluctuations in growth rate in one regime, but not the other. For droplet epitaxy, Zhou, Jesson et al. used in-situ microscopy of GaAs to observe how different structures form. In particular, for the exotic double-ring structures, they found that the outer ring grows in an extended zone outside the droplet. For both nanowire growth and droplet epitaxy, the surprising experimental behavior is reproduced and explained theoretically, as arising from the competition between evaporation and diffusion on the surface, with very different kinetics for the group V vs group III species.