The thermodynamics of trace element partition among coexisting phases is reviewed. Particular attention is paid to partition between crystalline solids and coexisting liquid phases. Extensive use is made of partition coefficients as defined by the equation D = ( Tr/Cr) sTr/CrL where ( Tr/Cr) s is the ratio of trace element to carrier element in the solid phase and ( Tr/Cr) L is the ratio of trace element to carrier element in the liquid. The effect of temperature, pressure and phase composition on the numerical value of D is discussed. If the trace element is altervalent, the relationships are more complicated in the case of solids with ionic bonding due to the requirement of electrical neutrality. The effect on D of maintaining a charge balance by (1) concomitant substitution of other trace elements and (2) by the formation of lattice vacancies, is considered. Both possibilities lead to expressions for D which are more complex than in the simple case in which the trace element and carrier element are of the same valence. The incorporation of an altervalent trace element in a crystal lattice in the form of a complex ion may in some instances lead to expressions for D that are simpler than those obtained in cases where the altervalent trace element substitutes directly for a lattice ion. Trace element partition between coexisting solid phases is also discussed. The effect of variations in the compositions of the solid phases on the partition is considered. The partition may depend on composition in a complicated way even though each solid phase may be considered an ideal solution with respect to variations in major components. If, in the crystallization of the solid phase from a liquid, the interior portions of the crystals do not maintain equilibrium with the liquid, trace elements may be distributed in the solid according to the logarithmic law. The numerical value of the logarithmic partition coefficient is dependent on the degree of supersaturation of the liquid solution. The value approaches the equilibrium value of D in cases where the solution is only infinitesimally supersaturated during crystallization. Trace elements are distributed homogeneously on the growth of a crystal as a result of slow relief of supersaturation of a non-agitated solution, but are distributed according to the logarithmic law if the crystal grew from a solution of constant supersaturation by a process such as evaporation. The theoretical basis for this difference is discussed. Applications of theory to geologic problems are reviewed and summarized. The distribution of trace elements between coexisting minerals can be made use of in geologic thermometry and barometry and to determine if a mineral assemblage represents an equilibrium assemblage. Trace element distribution among minerals in metamorphic terranes should be dependent on metamorphic grade. The data available seem to confirm this dependence. In the crystallization of an igneous rock mass it is to be expected that the distribution of trace elements will follow the logarithmic law. Curves based on the data of Wager and Mitchell, (1951) show that the distribution of trace elements in the Skaergaard intrusion of eastern Greenland does in fact closely follow the logarithmic law. Data from other intrusions also suggest that the logarithmic law is adhered to. It is possible that detailed studies of trace element distribution in granite bodies might be effective in distinguishing a magmatic from a metasomatic origin.