Nanostructures involving dielectric materials play an increasingly important role in numerous fields of science and technology. Prominent examples are ultra-precision machined optical surfaces, high-k dielectrics and diamond in microelectronics, catalytic surfaces and insulating substrates for sensor applications and molecular electronics. Dynamic scanning force microscopy (SFM) operated in the so-called non-contact mode is the method of choice for an atomic scale characterisation of such structures. The method of dynamic SFM is introduced as the only analysis tool capable of atomic resolution imaging of insulating surfaces and nanostructures. The state of the art in highest resolution dynamic SFM on insulators and challenges for future developments are illustrated for examples from different fields of application. While a detailed interpretation and quantitative understanding of atomic contrast formation is demonstrated for fluoride surfaces, the formation and dynamics of surface defects is discussed for oxide surfaces.