Exhumation of high-pressure metamorphic rocks can take place with typical plate velocities of cm/year. This is consistent with a model of forced flow in a subduction channel. The (micro)structural record of exhumed metamorphic rocks indicates that stresses are generally too low to drive deformation of the bulk material by dislocation creep, according to a power-law rheology. Instead deformation appears to be localized in low-strength shear zones, and is dominated by dissolution precipitation creep or fluid assisted granular flow, implying a Newtonian rheology. 1D modeling shows that the effective rheology of the material in the subduction channel has a significant influence on the rate of exhumation. When the subduction flux either equals or exceeds the return flux, the maximum exhumation rate for Newtonian behavior of the material is at least twice as high (~1/3 of the subduction burial rate) compared to that for power-law creep (~1/6 of the subduction burial rate).