The flow of concentrated suspensions of noncolloidal particles in viscous Newtonian fluids gives rise to shear-induced particle diffusion which can generate a nonuniform particle concentration profile within the sample being sheared even under creeping how conditions. This diffusive process owes its existence to the fact that the motion of a given particle within the suspension acquires a random component, as a result of the hydrodynamic interactions among the particles the positions of which are also random. We distinguish three such diffusive phenomena; (a) self-diffusion of a marked particle in a suspension of uniform concentration; (b) diffusion from regions of high concentration to low; and (c) diffusion from regions of high shear to low. As a consequence of (b) and (c), when a well-mixed suspension of neutrally buoyant particles is made to flow in a long tube or channel, a fully developed particle concentration profile is attained in which the concentration increases monotonically from the wall to the center. The effective viscosity of the suspension adjacent to the wall is thereby reduced and hence, for a given volumetric flow rate, the pressure drop in such a system is significantly lower than if the particles were uniformly distributed. These diffusive effects are also responsible for the phenomenon of viscous resuspension whereby an initially settled bed of heavy particles in contact with a clear fluid above it can be resuspended under the action of a shear flow. Several additional consequences of shear-induced particle diffusion in flowing concentrated suspensions are presented and then discussed.