This talk will be devoted to the effective large-scale behavior of suspensions of rigid particles in Stokesian fluids. Such systems are ubiquitous both in nature and in practical applications, and are well known to give rise to complex rheological behaviors, in particular to non-Newtonian effects. The main source of complexity is that particles are not point-like and that their interactions via the surrounding fluid flow are thus multibody in nature. Another difficulty lies in the long-range nature of these interactions, which means that renormalization is necessary to express various effective properties. We will address the derivation of so-called Doi models in dilute mean-field regime, the limitations of such effective theories, and the description of effective semi-dilute corrections.