A major outstanding challenge in quantum science is the development and refinement of techniques to control interactions among quantum particles, which will be a key ingredient in quantum information processing and laboratory studies of quantum many-body physics. This talk will describe two atom-based platforms for studying artificial spin-spin interactions. Using trapped atomic ions, we implement tunable long-range spin-spin interactions mediated by optical dipole forces, which form the backbone of current quantum simulations of magnetism. This platform has enabled sophisticated manipulations of more than 20 spins, and is additionally the first platform to support quantum simulations of integer-spin chains. A separate set of experiments builds on a hybrid system in which single photons, confined to sub-wavelength dimensions with a photonic crystal cavity, are coupled to single trapped neutral atoms. Extending this architecture to multiple atoms will enable photon-induced quantum gates, and even tunable spin-spin interactions, between distant atoms.