Suspensions are comprised of mesoscale particles of size from a few nanometres to a micron suspended in a fluid of molecular particles. The composite system is an example of a so-called complex fluid. Apart from technological interest, such systems are adjustable model systems in which physicists can study both equilibrium and non-equilibrium statistical mechanics of an unusual kind. The non-equilibrium motion of the mesoparticles defines a kind of many-body dynamical system many of whose properties remain unknown. I will give an introduction to some of the interesting questions that one can ask about these systems and to some of the computer simulation studies that can be used to describe them.