SIRPalpha is an inhibitory receptor present on myeloid cells that interacts with a widely distributed membrane protein CD47. The activating member SIRPbeta, despite extensive sequence similarity to SIRPalpha in the extracellular region, shows negligible binding to CD47. The SIRPalpha/CD47 interaction is unusual in that it can lead to bidirectional signalling through both SIRPalpha and CD47. This review concentrates on the interactions of SIRPalpha with CD47 where recent data have shed light on the structure of the proteins including determining why the activating SIRPbeta does not bind CD47, evidence of extensive polymorphisms and implication for the evolution and function of this protein and paired receptors in general. The interaction may be modified by endocytosis of the receptors, cleavage by proteolysis and through interactions of surfactant proteins.