Recent experiments on a class of atomically-thin two-dimensional materials, called moiré superlattice systems, have uncovered an entirely new and fascinating world of enigmatic strong-correlation physics and superconductivity. This project will develop theoretical models to explain these intriguing experimental observations. Numerical simulations will play an important role in guiding the theoretical models. An overarching goal is also to explore what lessons we can learn from moiré materials that advance our understanding of other paradigmatic strongly-correlated electron materials such as e.g. the copper-oxide superconductors.