The non-Newtonian shear rheology of colloidal dispersions is the result of the competition and balance between hydrodynamic (dissipative) and thermodynamic (conservative) forces that lead to a non-equilibrium microstructure under flow. We present the first experimental measurements of the shear-induced microstructure of a concentrated near-hard-sphere colloidal dispersion through the shear thickening transition using small-angle neutron scattering (SANS) measurements made in three orthogonal planes during steady shear. New instrumentation coupled with theoretical derivations of the stress-SANS rule enable rigorous testing of the relationship between this non-equilibrium microstructure and the observed macroscopic shear rheology. The thermodynamic and hydrodynamic components of the stress that drive shear thinning, shear thickening and first normal stress differences are separately defined via stress-SANS rules and compared to the rheological behaviour of the dispersion during steady shear. Observations of shear-induced hydrocluster formation is in good agreement with Stokesian dynamics simulation results by Foss & Brady (J. Fluid Mech., vol. 407, 2000, pp. 167–200). This unique set of measurements of shear rheology and non-equilibrium microstructure of a model system provides new insights into suspension mechanics as well as a method to rigorously test constitutive equations for colloidal suspension rheology.