Hydrofractures, or hydraulic fractures, are fractures where a significantly elevated fluid pressure played a role in their formation. Natural hydrofractures are abundant in rocks and are often preserved as magmatic dykes or sills, and mineral-filled fractures or mineral veins. However, we focus on the formation and evolution of non-igneous hydrofractures. Here we review the basic theory of the role of fluid pressure in rock failure, showing that both Terzaghi’s and Biot’s theories can be reconciled if the appropriate boundary conditions are considered. We next discuss the propagation of hydrofractures after initial failure, where networks of hydrofractures may form or hydrofractures may ascend through the crust as mobile hydrofractures. As fractures can form as a result of both tectonic stresses and an elevated fluid pressure, we address the question of how to ascertain whether a fracture is a hydrofracture. We argue that extensional or dilational fractures that formed below c. 2–3 km depth are, under normal circumstances, hydrofractures, but at shallower depth they may, but must not be hydrofractures. Since veins and breccias are often the products of hydrofractures that are left in the geological record, we discuss these and critically assess which vein structures can, and which do not necessarily, indicate hydrofracturing. Hydrofracturing can suddenly and locally change the permeability in a rock by providing new fluid pathways. This can lead to highly dynamic self-organization of crustal-scale fluid flow.