Anatectic stromatic migmatites have a symmetrical layered structure with a low ratio of thickness to length and a periodicity, features that have not been explained satisfactorily but which are related to physical processes of melt segregation. We evaluate the compaction model for segregation as it applies to migmatites and develop models for melt segregation based upon convection driven by volume change and upon advection down pressure gradients that result from applied differential stress acting on an anisotropic multilayer protolith. Compaction by gravity‐driven two‐phase flow results in asymmetric separation, yields calculated segregation times that are slow or geologically unreasonable, and yields relative volumes that are not consistent with the abundance of leucosome seen in natural migmatites. Although calculated segregation times for “very wet” granite might allow segregation by compaction, some driving force in addition to gravity is needed to cause widespread melt segregation in the crust. For segregation at low volume fraction of melt, we develop a two‐dimensional two‐phase (matrix and fluid) viscous flow cell model (length much greater than thickness) with phase changes which predicts either expansion or contraction convection (depending on whether volume change, ΔVr, is positive or negative). Convection leads to melt segregation to form a stromatic structure in a geologically reasonable timescale. At moderate volume fraction of melt, segregation may occur by filter pressing in compositionally layered rocks in response to applied differential stress. Melt migration is by porous medium flow driven by differences in mean normal stress between the layers, as a consequence of differences in rheology, and shear‐enhanced matrix collapse. Calculated segregation rates are fast, and the model yields adequate volume of leucosome. The positive ΔVr for volatile phase‐absent melting reactions under crustal pressures promotes melt escape, unless extensional deformation facilitates melt accumulation. If the rate of melt production exceeds the rate of melt escape, then the increase in melt pressure may lead to melt‐enhanced embrittlement and fracture, and melt may migrate out of the system. In contrast, water‐rich volatile phase‐present melt‐producing reactions have a negative ΔVr, which promotes melt retention after segregation, unless deformation generates melt escape pathways. Evolution of stromatic structure through anatectic erosion of mesosome by increasing the melt fraction in situ may lead to breakdown of the solid matrix and will lead to instability due to buoyancy, and magma may become mobile and entrain residual material (“restite”).