The progress in applications of density functional methods to problems of materials for heterogeneous catalysis as well as to their adsorption properties and reactivity is overviewed. Transition metal surfaces (Cu, Ru, Pd, Pt, Pd/Zn, Pd/Pt), metal oxide surfaces (MgO, NiO) and supported d-metal particles (atoms, Pd nanosize clusters) are taken as examples of catalytic substrates. Reactants/adsorbates considered range from single atoms, diatomic molecules, ammonia and small unsaturated hydrocarbons to more complex such as carbonate and urea molecules. Results of cluster- and slab-model density functional calculations chosen from various theoretical and experimental groups illustrate impressive achievements of the past decade in selected aspects of theory in heterogeneous catalysis. Also, some problems and limitations of the density functional description are alluded. (c) 2005 Elsevier B.V. All rights reserved.