Abstract A primary goal of geochemistry is the understanding of natural chemical differentiation through the chemical analysis of geological materials. Of particular interest to the geochemist are trace elements ( i.e . those present at concentrations of less than 0.1% by weight) which behave essentially as passive tracers during differentiation, and whose distribution can therefore yield process-specific information. Interpreting and modelling trace-element data requires quantitative information on how elements partition between coexisting phases, such as minerals and melts. Partitioning in turn depends on the energetics of trace-element incorporation into minerals and melts. With the advent of new analytical techniques and enhanced computer power our understanding in this field has increased substantially over the last two decades, to the extent that we can now offer greatly enhanced interpretative and modelling tools for the trace element geochemist. In this chapter we will attempt to summarise the state-of-the-art, with particular emphasis on new computational approaches. We begin by outlining experimental and analytical methods of investigating partitioning, delineate the principal controls on element partitioning, and discuss simple lattice strain models of trace element incorporation into minerals. The rest of the chapter is devoted to the development of atomistic computer simulation techniques and their application to the problem of trace element incorporation. The extent to which these approaches can reproduce the experimental observations is evaluated. Our focus is high-temperature silicate mineral-melt or mineral-mineral partitioning of trace cations, although our findings can be generalised to lower temperatures and non-silicate fluids and anions.