Superhydrophobic and superoleophobic surfaces have so far been made by roughening a hydrophobic material. However, no surfaces were able to repel extremely-low-energy liquids such as fluorinated solvents, which completely wet even the most hydrophobic material. We show how roughness alone, if made of a specific doubly reentrant structure that enables very low liquid-solid contact fraction, can render the surface of any material superrepellent. Starting from a completely wettable material (silica), we micro- and nanostructure its surface to make it superomniphobic and bounce off all available liquids, including perfluorohexane. The same superomniphobicity is further confirmed with identical surfaces of a metal and a polymer. Free of any hydrophobic coating, the superomniphobic silica surface also withstands temperatures over 1000°C and resists biofouling.