Magmas readily react with their surroundings, which may be other magmas or solid rocks. Such reactions are important in the chemical and physical evolution of magmatic systems and the crust, for example, in inducing volcanic eruptions and in the formation of ore deposits. In this contribution, we conceptually distinguish assimilation from other modes of magmatic interaction and discuss and review a range of geochemical (+/- thermodynamical) models used to model assimilation. We define assimilation in its simplest form as an end-member mode of magmatic interaction in which an initial state (t0) that includes a system of melt and solid wallrock evolves to a later state (tn) where the two entities have been homogenized. In complex natural systems, assimilation can refer more broadly to a process where a mass of magma wholly or partially homogenizes with materials derived from wallrock that initially behaves as a solid. The first geochemical models of assimilation used binary mixing equations and then evolved to incorporate mass balance between a constant-composition assimilant and magma undergoing simultaneous fractional crystallization. More recent tools incorporate energy and mass conservation in order to simulate changing magma composition as wallrock undergoes partial melting. For example, the Magma Chamber Simulator utilizes thermodynamic constraints to document the phase equilibria and major element, trace element, and isotopic evolution of an assimilating and crystallizing magma body. Such thermodynamic considerations are prerequisite for understanding the importance and thermochemical consequences of assimilation in nature, and confirm that bulk assimilation of large amounts of solid wallrock is limited by the enthalpy available from the crystallizing resident magma. Nevertheless, the geochemical signatures of magmatic systems-although dominated for some elements (particularly major elements) by crystallization processes-may be influenced by simultaneous assimilation of partial melts of compositionally distinct wallrock.