I will discuss a number of successful examples of computer simulation studies that help to understand the behavior of experimental colloidal suspensions. As a first example, I will show how simulations can help identify and predict novel crystal structures observed in experimental suspensions of oppositely charged colloids. The structures include analogs of known binary atomic structures, doped fullerene C₆₀ structures, but also novel structures that do not have an atomic of molecular analog. Second, I use simulations to better understand the phase diagram of charged colloids in an external magnetic- or electric field, where the colloidal pair potential is dominated by the dipole-dipole interaction. As a third example, I will show that simulations on binary hard-spheres lead to a proposal of exciting experiments that could produce photonic crystals with the wavelength in the visible region. Finally, I will discuss how methods frequently used in theoretical colloid science could be used to study systems that are of interest in biology, such as viral capsid self-assembly and protein-protein interactions.