  This review is devoted to the large-scale rheology of suspensions of rigid
particles in Stokes fluid. After describing recent results on the definition of
the effective viscosity of such systems in the framework of homogenization
theory, we turn to our new results on the asymptotic expansion of the effective
viscosity in the dilute regime. This includes an optimal proof of Einstein's
viscosity formula for the first-order expansion, as well as the continuation of
this expansion to higher orders. The essential difficulty originates in the
long-range nature of hydrodynamic interactions: suitable renormalizations are
needed and are captured by means of diagrammatic expansions.
