Biological processes depend on specific recognition between molecules with carefully tuned affinities. Because of the complexity of the problem, binding affinities cannot reliably be computed from molecular structures. Modern biophysical techniques can decompose the problem to determine the thermodynamic contributions from protein, cognate ligand and solvent. Such studies applied to a model protein with a hydrophobic binding pocket have resulted in some surprising findings. For example, binding is not driven by the favourable entropic loss of solvent water from the binding pocket, but rather by favourable dispersion interactions arising from suboptimal hydration of the protein-binding pocket. Under these circumstances, one can anticipate particularly dramatic gains in binding affinity using shape complementarity to optimise solute-solute dispersion interactions, since these will not be offset by opposing solute-solvent dispersion interactions.