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Van der Waals (vdW) interactions play a prominent role in the structure and function of organic/organic and organic/inorganic interfaces. Their accurate determination from first principles, however, is a notoriously difficult task. Recently, a surge of interest in modeling vdW interactions has led to promising theoretical developments. This article reviews the state-of-the-art of describing vdW interactions by density-functional theory with respect to accuracy and practicability. The performance of the different methods is demonstrated for simple systems, such as rare-gas dimers and small organic molecules. The nature of binding at organic/inorganic interfaces is then exemplified for the perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) molecule at surfaces of coinage metals. This fundamental system is the best-characterized organic molecule/metal interface in experiment and theory. We emphasize the …