Kelvin Force Probe Microscopy (KPFM) is a local scale advanced characterisation technique derived from atomic force microscopy, and is the focus of much research interest. It allows measurement of the contact potential of a surface with a resolution of the order of nanometres, yielding high resolution surface work function maps. Analysis of these maps allows the extraction of information on the electronic band structure and transport properties of materials and interfaces at the local scale. The technique is however highly sensitive to surface properties and in particular to surface state distributions. Therefore, the interpretation of contact potential variations across material and doping interfaces is complex. This paper presents a review of the field of KPFM methods and their analysis by modelling techniques. We review analytical approximations in a first approach for understanding of the physics of the KPFM technique and its interpretation. We then progress to more advanced KPFM modelling, which involves simulating the two-dimensional KPFM scanning process by sequentially scanning the atomic probe across the surface thereby reproducing the spatial extent of the experimental method. The two-dimensional description allows the inclusion of atomic probe geometry and the resulting impact on the resolution. The numerical methods allow a description of surface defect properties in terms of distributions in the gap, as well as descriptions of dopant species in terms of their energy distributions and capture cross sections or lifetimes. Applications of these methods are considered with a focus on photovoltaic applications, for the dominant materials in the field including group IV, III-V and concluding with considerations for emerging materials such as perovskites.