Experimental and theoretical work on the rheological properties of suspensions are reviewed. Attention is focused on systems consisting of rigid, neutrally buyoant particles suspended in Newtonian fluids; no restrictions, however, are placed on the concentration of the particles or on the forces acting in the suspension. The assumption that an effective viscosity depending solely on the volume fraction of the particles suffices to describe the rheology of suspensions is examined and shown to be inadequate. Indeed, the experimental evidence strongly supports the view that suspensions behave macroscopically as non-Newtonian fluids whose rheological properties are influenced by a large number of factors; these factors are listed. The various theories that have been put forward to explain the flow of suspensions are discussed, with particular emphasis being placed on the nature of the approximations made, so that purely empirical formulas can be clearly separated from those having a theoretical basis. Suggestions for future work, both theoretical and experimental, are provided.