The study of magmatic processes is at a juncture. New continuum models for the complex physics of crystallization and melting with convection and crystal‐melt segregation are now available, and the models are amenable to exploration by numerical methods. These models, which were largely developed in the fields of material science and mechanical engineering, will allow petrologists to consider a wide range of transport phenomena: crystal settling with reaction as fully multiphase flow, combined thermal and compositional buoyancy with realistic material property variations, open system and eruptive behavior and the appropriate system geometry and boundary conditions. The traditional notions of magma chambers as large vats of near liquidus material is being replaced by models where a substantial portion of the chamber may consist of a crystal‐melt mush, subject to reintrusion or mobilization. Percolative flow and reaction in this mush, including contaminants, may be as important as near‐liquidus processes in driving petrological diversity. Thus simple dimensionless numbers are of little utility in describing the vigor or style of magmatic processes. Melting of the crust following intrusion by basalt can be considered in light of two end‐members: the large sill or tabular mafic magma body and intrusion of basalt as sequences of spatially and temporally over lapping dikes. Although more commonly cartooned, the large sill type may not be nearly as efficient as repeated diking in driving crustal melting, magma mixing, and mingling. The greatest challenge for those studying magma dynamics will be to key the models to well‐constrained geological examples and to raise the sophistication of the content of these models in light of well‐defined tests that have geological significance.