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 crucial importance of a balanced description of both geometry and electronic structure in order to understand and model the properties of such systems. Finally, the relevance of vdW interactions to the function of actual devices based on interfaces is discussed.