We review first-principles calculations relevant to the adsorption of aromatic molecules on metal surfaces. Benzene has been intensively studied on a variety of substrates, providing an opportunity to comment upon trends from one metal to another. Meanwhile, calculations elucidating the adsorption of polycyclic aromatic molecules are more sparse, but nevertheless yield important insights into the role of non-covalent interactions. Heterocyclic and substituted aromatic compounds introduce the complicating possibility of electronic and steric effects, whose relative importance can thus far only be gauged on a case-by-case basis. Finally, the coadsorption and/or reaction of aromatic molecules is discussed, highlighting an area where the predictive power of theory is likely to prove decisive in the future.