Knowledge of the surface composition and atomic geometry is a prerequisite for understanding the physical and chemical properties of modern materials such as those used in, for example, heterogeneous catalysis, corrosion resistance, sensors, and fuel cells. To understand the function of surfaces under realistic conditions, it is crucial to take into account the influence of environmental gas at finite (possibly high) temperatures and pressures. Recent experimental and theoretical studies have shown that when transition metal surfaces are exposed to high oxygen pressures, thin oxide-like structures can form which may have little similarity to the bulk oxides, and thus possess unique chemical and physical properties. Given that technological oxidation catalysis typically involves oxygen-rich conditions, such structures may be present, and in fact be the active material for the reaction, as opposed to the traditionally believed pure metal. Using the approach of ab initio atomistic thermodynamics, free energy phase-diagrams for oxygen/transition metal systems in (T, p)-space ranging from ultra-high vacuum to technically relevant pressures, p, and temperatures, T, are discussed. In addition, results of ab initio statistical mechanical schemes, namely, the Lattice-gas Hamiltonian plus Monte Carlo (MC) simulations, are presented for oxygen/transition metal and alkali-atom/metal systems, where for the latter, the recently introduced "Wang-Landau" algorithm is employed, which affords an accurate estimation of the density of (configurational) states, therefore allowing a direct determination of all major thermodynamic functions. (c) 2005 Published by Elsevier B.V.