Current understanding of non-wettability of surfaces is presented and discussed. Three types of non-wettability are analysed: superhydrophobicity (drops on rough, hydrophobic surfaces), superhygrophobicity (drops on rough, hygrophilic surfaces), and under-water superhydrophobicity (rough, hydrophobic surfaces submerged in water). It is shown, based on quantitative work, that non-wettability must indeed be associated with the Cassie–Baxter state, and may be qualitatively defined by requiring the wetted area to be minimal. A quantitative definition is yet to be developed. The analysis is presented in terms of thermodynamic equilibrium and stability. To gain thermodynamic stability, the roughness geometry has to conform to a certain mathematical condition (for example, convex protrusions enable it while concave dents do not). The problem of optimal roughness geometry, including the issue of multi-scale roughness, is also discussed, concluding that the detailed optimal topography of non-wettable surfaces is yet to be elucidated. Finally, the fundamental principles underlying non-wettability are shown to be useful as design-guiding principles.