  Colloidal dispersions are commonly encountered in everyday life and represent
an important class of complex fluid. Of particular significance for many
commercial products and industrial processes is the ability to control and
manipulate the macroscopic flow response of a dispersion by tuning the
microscopic interactions between the constituents. An important step towards
attaining this goal is the development of robust theoretical methods for
predicting from first-principles the rheology and nonequilibrium microstructure
of well defined model systems subject to external flow. In this review we give
an overview of some promising theoretical approaches and the phenomena they
seek to describe, focusing, for simplicity, on systems for which the colloidal
particles interact via strongly repulsive, spherically symmetric interactions.
In presenting the various theories, we will consider first low volume fraction
systems, for which a number of exact results may be derived, before moving on
to consider the intermediate and high volume fraction states which present both
the most interesting physics and the most demanding technical challenges. In
the high volume fraction regime particular emphasis will be given to the
rheology of dynamically arrested states.
