Experiments reveal the existence of metallic bands at surfaces of metals and insulators. The bands can be doped externally. We review properties of surface superconductivity that may set up in such bands at low temperatures and various means of superconductivity defection. The fundamental difference as compared to the ordinary superconductivity in metals, besides its two-dimensionality lies in the absence of the center of space inversion. This results in mixing between the singlet and triplet channels of the Cooper pairing.