The present work proposes the use of anisotropically permeable substrates as a means to reduce turbulent skin friction. We conduct an a priori analysis to assess the potential of these surfaces, based on the effect of small-scale surface manipulations on near-wall turbulence. The analysis, valid for small permeability, predicts a monotonic decrease in friction as the streamwise permeability increases. Empirical results suggest that the drag-reducing mechanism is however bound to fail beyond a certain permeability. We investigate the development of Kelvin-Helmholtz-like rollers at the surface as a potential mechanism for this failure. These rollers, which are a typical feature of turbulent flows over permeable walls, are known to increase drag, and their appearance to limit the drag-reducing effect. We propose a model, based on linear stability analysis, which predicts the onset of these rollers for sufficiently large permeability, and allows us to bound the maximum drag reduction that these surfaces can achieve.