It is only recently that the wealth of structural phenomena at the surfaces of solids has begun to be revealed with atomic resolution. The pervasive importance of solid surfaces in processes ranging from energy conversion, corrosion and microchip technology to electrochemistry and heterogeneous catalysis is widely appreciated. Equally, it is recognised that a detailed understanding of these processes requires a description of the location of all the atoms which constitute the surface. In the earliest models it was assumed that substrate atoms in a given exposed plane of a single crystal material would be located at bulk site positions. Adsorption onto such surfaces would proceed as with checkers on a checkerboard, producing filled and unfilled sites appropriate for treatment with Ising-type models.