We review the results of theoretical modelling of scanning force microscopy and discuss the possibility of obtaining atomic and chemical resolution in contact and non-contact mode SFM, and a related issue of a working model for interpretation of SFM images. As a prototype system we consider the interactions of hard tips with softer alkali halide surfaces in UHV. We briefly review experimental data, then discuss results of static atomistic simulations and molecular dynamical modelling of contact SFM to test some of the assumptions of intuitive SFM models. Then we illustrate the shortcomings of contact SFM by considering an image of a point defect. The mechanism of resolution in non-contact SFM and the effect of avalanche tip-surface adhesion are discussed next. We conclude by discussing the status of SFM with atomic resolution.