Moiré superlattices, formed by stacking two-dimensional materials with a small interlayer twist, have emerged as a remarkably flexible platform to engineer and study novel quantum phases of matter. In this talk, I will describe single-electron transistor microscopy of semiconducting moiré materials, which host a variety of correlated phases ranging from electron solids to topological fluids. By measuring how these states respond to experimental tuning knobs such as twist angle and applied electromagnetic fields, we can relate their properties to the microscopic character of the underlying bands. This enables us to disentangle the respective roles played by the moiré superlattice and the constituent material properties in stabilizing distinct ground states.