Volcanism, mantle convection and plate tectonics are tightly coupled on Earth. This coupling motivates a theory that consistently describes creeping solid deformation, phase change between solid and liquid, and liquid segregation. The theory was derived about 40 years ago and has been used to model various aspects of magma/mantle dynamics. In this talk, I give a summary of the physical context and the derivation of the governing equations, highlighting key aspects of the physics and their emergent scales. I then discuss two pattern-forming instabilities of this system and their relationship with observations. The first is a mechanical instability that is observed in laboratory deformation experiments on partially molten rock. It leads to high-porosity bands orientated at a (surprisingly) low angle to the shear plane. I discuss rheological hypotheses to explain this observation, focusing on one that invokes an anisotropic, Coble-creep viscosity. The second instability arises by reactive infiltration of corrosive magma. As magma segregates due to buoyancy, progressively lower pressures increase the liquid solubility of silica. This causes a reactive flow whereby magma dissolves the porous matrix through which it percolates. High-flux channels emerge and provide a fast pathway for magma transport, with the potential for chemical disequilibrium. Time permitting, I discuss possible coupling of these instabilities, as well as other complexities such as mantle lithological heterogeneity and complex rheological models of the mantle-lithosphere system.