Methods for simulation of natural differentiation processes have been an object of study for most of the history of igneous petrology. With the advent of quantitative geochemical data on experimental systems, the models used by petrologists have moved progressively from graphical (i.e., phase diagrams) to numerical methods [e.g., Roeder and Emslie, 1970; Stormer and Nicholls, 1978]. Even developments in graphical methods have entailed increased complexity in the projection of compositional data [e.g., Grove et al., 1982]. This article summarizes current developments in some of the most recent nongraphical models of phase equilibria. The most critical component of these models is the method used to calculate the melt component activities.