Magmas undergoing shear are prime examples of flows that involve the transport of solids and gases by a separate (silicate melt) carrier phase. Such flows are called multiphase, and have attracted much attention due to their important range of engineering applications. Where the volume fraction of the dispersed phase (crystals) is large, the influence of particles oil the fluid motion becomes significant and must be taken into account in any explanation of the bulk behaviour of the mixture. For congested magma deforming well in excess of the dilute limit (particle concentrations >40%, by volume), Sudden changes in the effective or relative viscosity call be expected. The Picture is complicated further by the fact that the melt phase is temperature- and shear-rate-dependent. In the absence of a Constitutive law for the flow of congested magma under an applied force, it is Jar from clear which of the man), hundreds of empirical formulae devised to predict the rheology of suspensions as the particle fraction increases with time are best suited. Some of the more commonly used expressions ill geology and engineering are reviewed with an aim to home in oil those variables key to ail improved understanding of magma rheology. These include a temperature, compositional and shear-rate dependency of viscosity of the melt phase with the shear-rate dependency of the crystal (particle) packing arrangement. Building oil previous formulations, a new expression for the effective (relative) viscosity of magma is proposed that gives users the option to define a packing fraction range as a function of shear stress. Comparison is drawn between processes (segregation, clustering, jamming), common ill industrial slurries, and structures seen preserved in igneous rocks. An equivalence is Made Such that congested magma, viewed in purely mechanical terms as a high-temperature slurry, is an inherently non-equilibrium material where flow at large Peclet numbers may result in shear thinning and spontaneous development of layering.