The rheology of concentrated, aggregated colloidal suspensions is determined through particulate simulations. Aggregating systems experience a large viscous enhancement over nonaggregating systems, this being due to the increase in the component of the viscosity arising from the repulsive colloid (thermodynamic) forces when attractive forces are present. The shear behavior of aggregating systems, for colloid volume fraction 0.47 less than or equal to phi(c) less than or equal to 0.57, is characterized in the steady state regime over a wide range in shear rate, and is found to be power law, shear thinning eta similar to f(phi(c)) (gamma) over dot (-alpha) , where the shear thinning index alpha = 0.84 +/- 0.01. The effect of volume fraction enters as f(phi(c)) = (1- phi c/phi(max))(-1) with phi(max) = 0.64, the value of random close packing; similarly, the viscosity also scales with the potential well depth as a power law, of index . Consequently, we are able to deduce the full constitutive relation for this power law behavior. The associated structural features which emerge as a result of the imposed shear are identified with the rheology. The shear thinning regime crosses over into a state of ordered phase flow at high shear rates likewise simulations of hard sphere fluids. We also show that the high-shear ordered configurations appear to be a function of colloid concentration, with a transition from string phase order through to layered phases as phi(c) increases.