Abstract Shear-wave splitting due to stress-aligned anisotropy is widely observed in the Earth’s crust and upper mantle. The anisotropy is the result of stress-aligned fluid-saturated grain-boundary cracks and pore throats in almost all crustal rocks, and we suggest by stress-aligned grain-boundary films of liquid melt in the uppermost 400 km of the mantle. The evolution of such fluid-saturated microcracks under changing conditions can be modelled by anisotropic poro-elasticity (APE). Numerical modelling with APE approximately matches a huge range of phenomena, including the evolution of shear-wave splitting during earthquake preparation, and enhanced oil recovery operations. APE assumes, and recent observations of shear-wave splitting confirm, that the fluid-saturated cracks in the crust and (probably) upper mantle are so closely spaced that the cracked rocks are highly compliant critical systems with self-organised criticality. Several observations of shear-wave splitting show temporal variation displaying extreme sensitivity to small stress changes, confirming the crack-critical system. Criticality has severe implications for many Solid Earth applications, including the repeatability of seismic determinations of fluid flow regimes in time-lapse monitoring of hydrocarbon production. Analysis of anisotropy-induced shear-wave splitting is thus providing otherwise unobtainable information about deformation of the inaccessible deep interior of the Earth.