Abstract: Analog quantum simulators use the native interactions between effective spins to study Hamiltonians. In most quantum simulators, the native interactions are local, limiting the connectivity between the spins. The capacity of engineering non-local interactions opens up possibilities to generate highly entangled states and study long-range spin physics. The first part of my talk focuses on engineering and characterizing Hamiltonians in trapped-ion systems, which feature intrinsic non-local interactions mediated by phonons. I will talk about a new experimental tool for probing pairwise interactions by shelving a subset of the ions into an auxiliary Zeeman level. I will also discuss a new strategy for estimating Hamiltonian parameters by implementing a quantum-quench protocol. The second part of my talk centers on engineering non-local interactions in the Rydberg array platform. I will introduce a novel high-finesse cavity designed for Rydberg arrays. The cavity has state-of-the-art single-atom cooperativity (\eta = 21) and will allow more than 50 atoms in the array, enabling the generation of non-local interactions mediated by light. I will discuss the potential applications in this new cavity platform.