High-temperature hydrothermal venting at the sea floor appears to be driven by heat transfer from shallow crustal magma chambers beneath the axis of the global mid-ocean ridge system. Models of magma-hydrothermal heat transfer indicate that high Rayleigh number cellular convection in a homogeneous porous medium cannot account for the heat flux in typical high-temperature (black smoker) vents. Single-pass models, in which the flow paths are controlled by faults and fracture zones of high permeability, are more effective at collecting the heat from the magma body and focusing it to a vent field; but models of this type, in which the boundary layer thickens in time as the magma chamber freezes, cannot easily explain the stability of temperature and vent fluid chemistry observed in some active vent systems. It may be that fractures generated by thermal stresses can foster the downward migration of the hydrothermal system into hot solidified magma. This process may help explain some of the geochemical data, but the physics of crack propagation in this context is not well understood.