Results are presented for light scattering studies of suspensions in a liquid of nearly hard colloidal spheres. Interparticle ordering or microstructure is determined for samples in equilibrium and undergoing both steady and oscillatory shear flows. Four basic structures are found to exist under these conditions: liquid‐like or amorphous, string‐like, sliding or randomly stacked layers, and face centered cubic. The conditions leading to these different microstructures is examined systematically and compared with predictions of microstructure for atomic and molecular or colloidal suspensions undergoing steady shear flow. Generally we find that ordering into layers at a finite shear rate is more pronounced as the volume fraction of particles increases. Equilibrium liquid‐like samples do not evidence a transition into a layer structure with increasing shear rate, and equilibrium crystalline samples do evidence a shear resisting face centered cubic ordering at small shear rates. For oscillatory shear flows we find that equilibrium liquid‐like samples could be induced to have a face centered cubic structure or layer structure depending on the amplitude and frequency of the shear flow. A microstructure phase diagram as a function of volume fraction of particles and oscillatory shear amplitude is constructed and compared with a simple model based on a strained face centered cubic lattice. Studies are presented which demonstrate the effect of shear history in producing desired microstructures.