Basic theoretical and some practical aspects of the interpretation of X-ray scattering experiments are described. Our focus is on model building and refinement associated with retrieving information related to electron density matrices from the measured data. The ill-posed nature of this inverse problem is emphasised and the physical significance, reliability and reproducibility of the properties obtained by data fitting are discussed through representative examples taken from recent studies. A special attention is devoted to the pseudoatom formalism widely used to interpret high-resolution single-crystal X-ray diffraction data to map the static electron distribution in solids. © Springer Science+Business Media B.V. 2012.