Block copolymers dissolved in a selective solvent form micelles that can be regarded as model colloidal dispersions because by tailoring the copolymer composition, the relative size of core and corona can be controlled. This enables the interaction potential to be varied, such that either hard or soft sphere ordering can be observed above the liquid–solid (sol–gel) transition. Here we review recent work on the structure and rheology of micellar phases formed by block copolymers in solution. First, the structure of solid and liquid micellar phases is considered, and its relationship to flow properties of gels and sols is discussed. Then the ordering of hard versus soft spheres is considered in the context of experimental phase diagrams for poly(styrene)–poly(isoprene) in decane and poly(oxyethylene)–poly(oxybutylene) diblock copolymers in water. The use of experiments in the linear viscoelastic regime to locate the gelation (liquid–solid) transition is then reviewed, and the application of measurements in the linear viscoelastic regime to study relaxation phenomena is also outlined. The nonlinear flow behaviour of micellar block copolymer solutions is then considered. In particular the focus is on the development of a yield stress in the solid phase, creep and stress relaxation measurements which throw light on flow mechanisms, and Fourier transform rheology which provides a quantitative measure of nonlinear viscoelasticity under oscillatory shear. Finally, an overview is provided of recent small–angle scattering experiments that have probed the mechanisms of macroscopic alignment of body–centred and face–centred cubic micellar phases subjected to large–amplitude oscillatory shear or steady shear in a Couette cell.