The rheology during the start-up and cessation of simple shear flow has been investigated for near hard-sphere colloidal suspensions. Simulations augmented by theoretical analysis are used to determine how the non-Newtonian stress development and relaxation depend on the microstructure. Accelerated Stokesian dynamics (ASD) and Brownian dynamics (BD) simulations are used for 0.05 <= Pe <= 500 in concentrated freely flowing suspensions; the Peclet number defining the ratio of shear to thermal motion is Pe = 3 pi eta(gamma) over dota(3)/kT with eta the suspending fluid viscosity, (gamma) over dot the shear rate, and kT the thermal energy. Theoretical predictions based on the Smoluchowski equation for dilute suspensions are made, and these are primarily used for comparison with results from BD simulations in which hydrodynamic interactions are neglected. For suspensions with hydrodynamics, simulations by ASD are used to probe start-up and flow cessation over a large range of Pe; these studies focus on solid volume fraction phi 0: 4, with more limited examinations at other phi. The use of both BD and ASD simulations allows us to discriminate hydrodynamic interaction effects on the suspension rheology. The Brownian stresses computed by either method exhibit overshoots of their steady state value during the start-up of shear flow. The overshoots occur at strain amplitudes which depend on Pe, and the overshoot is described by a model based on extension of the concept of cage-breaking from glass dynamics. Results from the relaxation of a sheared suspension show that the distortion of the pair distribution function from its equilibrium form has a fast radial relaxation and a slow angular relaxation. The various rheometric functions (relative viscosity; first and second normal stress differences) are found to respond on different timescales, reflecting their different dependences on the flow-induced structure. A re-examination of steady shear flow allows us to find normal stress differences which tend properly toward zero at small Pe, unlike prior work; the discrepancy is found to be due to finite size scaling, as small simulations used in prior work resulted in excessively large normal stress responses at small Pe. (C) 2017 The Society of Rheology.