A new generation of electron microscopes is able to explore the microscopic properties of materials and devices as diverse as transistors, turbine blades and interfacial superconductors. All of these systems are made up of dissimilar materials that, where they join at the atomic scale, display very different behaviour from what might be expected of the bulk materials. Advances in electron optics have enabled the imaging and spectroscopy of these buried interface states and other nanostructures with atomic resolution. Here I review the capabilities, prospects and ultimate limits for the measurement of physical and electronic properties of nanoscale structures with these new microscopes.