Basic molecular concepts in heterogeneous catalysis are illustrated by recent results from periodic and cluster density functional theory (DFT) calculations. For reactions on platinum surfaces, differences in the activation barriers found for ammonia activation are analysed in terms of bond-order conservation principles. The notion of early and late transition-states is introduced and used to understand the difference between step edges versus terrace activation. Another important concept relates to the stereoselectivity of a catalytic reaction. For immobilized organo-metallic complexes, the ligand-reactant interaction dominates the selectivity. We analyse activation by immobilized salen complexes and show that attachment of the catalytically active complex to the wall of a microporous system can dramatically affect the conformation of the ligand and hence selectivity. In zeolites we find that the match of shape and size of pre-transition-state structures with the zeolite cavity dominates the stereochemistry of the reaction.