Molecular recognition, binding and catalysis are often mediated by non-covalent interactions involving aromatic functional groups. Although the relative complexity of these so-called π interactions has made them challenging to study, theory and modelling have now reached the stage at which we can explain their physical origins and obtain reliable insight into their effects on molecular binding and chemical transformations. This offers opportunities for the rational manipulation of these complex non-covalent interactions and their direct incorporation into the design of small-molecule catalysts and enzymes.