Considerable progress has been made recently, using scanning tunnelling microscopy (STM), scanning tunnelling spectroscopy (STS) and local density functional theory (DFT), in examining the atomic structure and electronic properties of ultrathin insulating films. This article reviews pertinent results to date with special emphasis on ultrathin MgO films on Ag(001) surfaces. Using STS, the layer-by-layer resolved electronic structure up to 3 ML shows that the band gap of about 6 eV at the MgO surface develops within the first 3 ML confirmed by local density of states (LDOS) calculations. Using model calculations, the atomic species observed in STM on the MgO film are unambiguously identified. These results underline the importance of a combination of local spectroscopy, scanning probe techniques and local density of states calculations for the understanding of matter on the microscopic level.