Just as nanoparticles display properties that differ from those of bulk samples of the same material, ensembles of nanoparticles can have collective properties that are different to those displayed by individual nanoparticles and bulk samples. Self-assembly has emerged as a powerful technique for controlling the structure and properties of ensembles of inorganic nanoparticles. Here we review different strategies for nanoparticle self-assembly, the properties of self-assembled structures of nanoparticles, and potential applications of such structures. Many of these properties and possible applications rely on our ability to control the interactions between the electronic, magnetic and optical properties of the individual nanoparticles.