The term allostery was originally developed to describe structural changes in one binding site induced by the interaction of a partner molecule with a distant binding site, and it has been studied in depth in the field of enzymology. Here, we discuss the concept of action at a distance in relation to the folding and function of the solenoid class of tandem-repeat proteins such as tetratricopeptide repeats (TPRs) and ankyrin repeats. Distantly located repeats fold cooperatively, even though only nearest-neighbour interactions exist in these proteins. A number of repeat-protein scaffolds have been reported to display allosteric effects, transferred through the repeat array, that enable them to direct the activity of the multi-subunit enzymes within which they reside. We also highlight a recently identified group of tandem-repeat proteins, the RRPNN subclass of TPRs, recent crystal structures of which indicate that they function as allosteric switches to modulate multiple bacterial quorum-sensing mechanisms. We believe that the folding cooperativity of tandem-repeat proteins and the biophysical mechanisms that transform them into allosteric switches are intimately intertwined. This opinion piece aims to combine our understanding of the two areas and develop ideas on their common underlying principles. This article is part of a discussion meeting issue ‘Allostery and molecular machines’.