Receptor clustering is a well-established feature of transmembrane signalling. In some cellular systems, clusters form dynamically in response to activation by an extracellular ligand; in others, extensive 2-dimensional arrays of receptors persist for long periods of time on the cell surface. Compelling evidence has accumulated that the interactions between receptors within a cluster play an important role in the signalling process. Here, we review statistical mechanical models that describe how clusters may be generated and maintained by the equilibrium thermodynamic interactions between receptors, the extracellular ligands that bind to their periplasmic domains, and cytosolic 'adaptor proteins' that bind to the cytoplasmic domains of the receptors. We discuss how adaptor proteins might permit cells to exert control over the propensity of cluster formation, and to target clusters to specific locations on the cell surface. We further outline how differential interactions between active and inactive receptors can enhance the sensitivity of the cellular response through the mechanism of 'conformational spread'.