Colloidal dispersions are ubiquitous in everyday life (e.g. ink, milk or blood) and consist of mesoscopic particles, typically somewhere between ten nanometers and one micrometer in size, suspended in a solvent. Since the experiments of Robert Brown in 1827, in which he observed the irregular 'Brownian motion' of small suspended particles through his microscope, colloidal systems have proved a constant attraction to theorists from various disciplines (Einstein, Langevin, Smoluchowski, Onsager ...). Much of the appeal of colloidal systems arises from the fact that, in many ways, they behave like giant atoms, but with length- and time-scales which are much more accessible to experiment than their atomic counterparts. Colloidal dispersions provide flexible
model systems, which enable fundamental phenomena both in and out of equilibrium to be addressed.

In this talk I will discuss some recent progress in my ongoing theoretical effort to understand the nonequilibrium behaviour of simple model colloidal systems, with emphasis on the use of mechanical shearing as a means to drive the system out of equilibrium.  Of particular interest will be the nature of the two-point correlation functions in the nonequilibrium steady state and the stress relaxation of colloidal glasses following the cessation of flow.