During the past fifteen years there has been a dramatic increase in the number of different surfaces whose structures have been determined experimentally. For example, whereas in 1979 there were only 25 recorded adsorption structures, to date there are more than 250. This volume is therefore a timely review of the state-of-the-art in this dynamic field. Chapter one contains a compilation of the structural data base on surfaces within a series of tables that allows direct comparison of structural parameters for related systems. Experimental structural trends amongst both clean surfaces and adsorbate systems are highlighted and discussed. The next chapter outlines the successes of local density functional theory in predicting the relaxations and reconstructions of clean metal and semiconductor surfaces, and the behaviour of adsorbates such as hydrogen, oxygen and alkali elements on metal surfaces, thereby explaining some of the experimental trends observed within the database. These ab initio density functional calculations are of ground state properties at the absolute zero of temperature.Chapter three provides an introduction to finite temperature effects in a pedagogical review of current statistical mechanical treatments of phase transitions at surfaces, many of which display the prominent role of fluctuations or non-mean field behaviour. The final chapter discusses the relationship of the reactivity of a surface to its morphology and composition, which is particularly relevant to a fundamental understanding of catalysis.