The shear rheology of carbon nanotube suspensions is reviewed from the perspective of colloid and polymer science. In the semi-dilute to concentrated regimes, the nature of the equilibrium or quiescent state is often dominated by nanotube entanglement and strong attractive inter-particle interactions that favor the formation of a disordered network or gel. The strength of this network with respect to the applied stress dictates the development of mesoscale structural anisotropy, first through a global yield stress and then through a critical stress for homogenization. For concentrated suspensions, the nematic liquid-crystalline order anticipated for high-aspect-ratio rigid rods has been observed in a few select scenarios. The opportunity for deeper theoretical insight is emphasized and intuitive physical arguments are offered that might serve as a foundation for future study.