Abstract: High-impedance superconducting circuits provide a powerful platform for quantum computing and quantum simulations, combining strong nonlinearity, high coherence, and enhanced coupling to quantum degrees of freedom. I will provide an overview of my group's work on the design and application of such circuits based on Josephson junction arrays. In particular, I will discuss how Josephson junction arrays help us understand dielectric loss in fluxonium superconducting qubits, enable efficient bosonic quantum encoding, and facilitate simulations of quantum many-body problems.