When two van der Waals materials of slightly different orientations or lattice constants are overlaid, a moiré pattern emerges. The moiré pattern introduces a new length scale, many times the lattice constant of the original materials, for Bragg scattering of Bloch electrons in each layer.  This gives rise to moiré minibands and rich emergent phenomena. In this talk I will discuss recent experiments on angle-aligned semiconductor heterobilayers, which exhibit remarkable correlated insulating states. I will also discuss the prospect of using moiré superlattices as a Hubbard model quantum simulator.