This paper presents a general overview of flow in deformable porous media with emphasis on melt extraction processes beneath mid-ocean ridges. Using a series of simple model problems, we show that the equations governing magma migration have two fundamentally different modes of behaviour. Compressible two-phase flow governs the separation of melt from the solid and forms a nonlinear wave equation that allows melt to propagate in solitary waves. Incompressible two-phase flow governs small-scale mantle convection driven by lateral variations in melt content. The behaviour of both compressible and incompressible matrix deformation is demonstrated in the context of mid-ocean ridges to show that both mechanisms may explain the observation of the narrowness of ridge volcanism. These results also suggest that melt extraction is an inherently time dependent process that may account for the timing, volume and chemistry of volcanism.