Abstract: An efficient and scalable means of entangling atoms is to couple them to a single mode of light in an optical cavity. Such collective atom-light coupling naturally produces a single globally entangled state, such as a squeezed spin state, which can serve as a resource for enhancing clocks or sensors. However, many practical sensing tasks involve estimating more than a single parameter, and therefore benefit from advances in controlling the spatial structure of entanglement. I will report on experiments in which we program the network of entanglement within an array of atomic ensembles by combining global cavity-mediated interactions with local addressing. We demonstrate the flexibility of this approach for entanglement-enhanced sensing of spatially patterned fields and for engineering continuous-variable graph states. The minimal instance of such a graph state — an EPR entangled state — enables simultaneous sensitivity to perturbations in non-commuting observables for applications including ac and vector magnetometry. Benefiting from this sensitivity requires measuring nonlocal quantities, which we achieve via a cavity-enabled interaction-based readout scheme. I will also touch on applications of interaction-based readout in quantum simulation, which we illustrate by probing topological edge states with a cavity-based nonlocal interferometer.