The current status and future prospects of non-contact atomic force microscopy (nc-AFM) and Kelvin probe force microscopy (KPFM) for studying insulating surfaces and thin insulating films in high resolution are discussed. The rapid development of these techniques and their use in combination with other scanning probe microscopy methods over the last few years has made them increasingly relevant for studying, controlling, and functionalizing the surfaces of many key materials. After introducing the instruments and the basic terminology associated with them, state-of-the-art experimental and theoretical studies of insulating surfaces and thin films are discussed, with specific focus on defects, atomic and molecular adsorbates, doping, and metallic nanoclusters. The latest achievements in atomic site-specific force spectroscopy and the identification of defects by crystal doping, work function, and surface charge imaging are reviewed and recent progress being made in high-resolution imaging in air and liquids is detailed. Finally, some of the key challenges for the future development of the considered fields are identified.