Abundances of trace elements in extrusive igneous rocks may be used as petrological and geochemical probes of the source regions of the rocks if differentiation processes, partition coefficients, phase equilibria, and initial concentrations in the source region are known. The characteristic trace element signature that each mineral in the source region imparts on the magma forms the conceptual basis for trace element modeling. The task of the trace element geochemist is to solve mathematically the inverse problem. Given trace element abundances in a magma, what is the mode of its source region? The most successful modeling has been performed for small planetary bodies which underwent relatively simple igneous differentiation events. An example is the eucrite parent body, a planet which produced basalts at ⋍4.6 Gy. and has been quiescent ever since. This simple differentiation history permits the calculation of its bulk composition (a feldspathic peridotite) and has led to the tentative identification of asteroid 4 Vesta as the eucrite parent body. The differentiation of iron meteorite groups in parent body cores is amenable to similar treatment. Quantitative calculations are currently hampered by the paucity of experimentally determined solid metal/liquid metal partition coefficients. The ‘anomalous’ behavior of Cr, however, suggests that IIIA, B irons and main group pallasites equilibrated with troilite, spinel, ferromagnesian silicates, or some combination thereof. The moon has undergone more complex differentiation, and quantitative geochemical modeling is correspondingly more difficult. Nevertheless, modeling the two‐stage evolution of mare basalts raises the possibility that the primordial moon did not have chondritic relative abundances of such refractory elements as Ca, Al, U, and the rare‐earth elements. The nonchondritic element ratios are characteristic of planetary, not nebular, fractionation processes and are consistent with the derivation of the moon from a precursor planet, possibly the earth. Alternatively, they may be artifacts of our inadequate understanding of differentiation in a deep, rapidly convecting magma ocean. The enormous complexity of terrestrial evolution over geologic time generally precludes quantitative geochemical modeling of the earth. For example, calculations investigating the petrogenesis of calc‐alkaline andesites are restricted to limiting the range of plausible hypotheses. In cases where Nd isotopic systematics indicate that the source region of a basalt suite had an approximately chondritic Sm/Nd ratio (e.g., Columbia River Plateau), semiquantitative calculations of the nature of the mantle may be possible. Geochemical modeling may have predictive value for an unsampled planet such as Mercury which may have had a relatively simple ther