We have studied the flow behavior of a colloidal system with attractive interactions. Dilute suspensions of carbon black particles in nonpolar hydrocarbon solvents aggregate due to van der Waals forces and form colloidal gels. Under steady flow, these systems surprisingly display shear thickening above a critical shear rate, g^•_c , that is dependent on composition, solvent viscosity and the amount of stabilizing surfactant present in the system. The transition to shear thickening flow is marked by a sharp increase in the first normal stress difference, suggesting that hydrocluster formation, as observed in hard-sphere and repulsive systems, is not the mechanism here. We propose that shear thickening is instead due to hydrodynamic break-up of carbon black clusters which leads to an increase in the effective volume fraction of the suspension due to the fractal nature of the individual particle structure. This is supported by optical observations which show a finely dispersed suspension microstructure at high shear rates, g^• > g^•_c , in contrast to the densified aggregated clusters observed at lower shear rates. The elasticity of gels formed after pre-shearing above g^•_c shows a power law dependence on pre-shear stress. We account for these results with a simple scaling argument that rationalizes the elastic modulus in terms of the cluster number density, as defined by the hydrodynamic breakup of clusters beyond the shear thickening transition. Abrupt cessation of shear in systems under steady flow produces a quench into a gelled state, accompanied by the development of internal or residual stresses. We study the time-dependence of these stresses and find that they relax with a weak power law decay over timescales on the order of 10³ s. These stresses are thought to play a key role in the dynamics of disordered, non-ergodic systems and are a topic of continued study.