Coupling many atoms to a single mode of light provides an efficient means of spreading quantum information across an extended many-body system. I will report on experiments in which we harness photons in an optical cavity to mediate “flip-flop” interactions among distant spins in a millimeter-long cloud of laser-cooled atoms. We characterize the spin-exchange interactions via quench dynamics and imaging of the local magnetization, demonstrating optical control of the interactions' strength and sign. Furthermore, we observe signatures of correlated pair creation in Zeeman states of a spin-1 system, a light-mediated analog of collisional spin mixing in Bose-Einstein condensates. In contrast to direct collisional interactions, non-local photon-mediated interactions offer unprecedented opportunities for engineering the spatial structure of spin-spin couplings and correlations. I will describe prospects for tailoring atom-light interactions to enable new directions in quantum simulation and to generate new resources for quantum-enhanced sensing.