Suspensions are fluids containing a large amount of solid particles that interact hydrodynamically through the suspending fluid, and non-hydrodynamically upon direct contact. Interestingly, when sheared periodically at low Reynolds number, the particle dynamics can undergo a reversible-irreversible transition (RIT) characterized by a critical strain amplitude: below this amplitude, all particles return to their original positions after each shear cycle; above it, they diffuse. In this talk, I will describe the corresponding rheology of this process. Specifically, I will show that there are at least four rheological signatures at the onset of RIT, and they are related to the emergent dynamics through a shear-induced microstructure that tends to be hyperuniform at steady state. Furthermore, I will discuss the possibility of a second transition threshold and the associated suspension rheology, if the particles are adhesive. In general, these results suggest that non-hydrodynamic interactions dictate the particle dynamics while hydrodynamic interactions influence the rheology.