Title: A Microscopic Perspective on Moiré Materials

Abstract: Contemporary quantum materials research is guided by themes of topology and of electronic correlations. A confluence of these two themes is engineered in "moir\'e materials", an emerging class of highly tunable, strongly correlated two-dimensional (2D) materials designed by the rotational or lattice misalignment of atomically thin crystals. In moir\'e materials, dominant Coulomb interactions among electrons give rise to collective electronic phases, often with robust topological properties. Identifying the mechanisms responsible for these exotic phases is fundamental to our understanding of strongly interacting quantum systems, and to our ability to engineer new material properties for potential future technological applications. In this Review, we highlight the contributions of local spectroscopic, thermodynamic, and electromagnetic probes to the budding field of moir\'e materials research. These techniques have not only identified many of the underlying mechanisms of the correlated insulators, generalized Wigner crystals, unconventional superconductors, moir\'e ferroelectrics, and topological orbital ferromagnets found in moir\'e materials, but they have also uncovered fragile quantum phases that have evaded spatially averaged global probes. Furthermore, we highlight recently developed local probe techniques, including local charge sensing and quantum interference probes, that have uncovered new physical observables in moir\'e materials.