<p>Receptors of insulin and insulin-like growth factors (IGFs) are receptor tyrosine kinases whose signalling controls multiple aspects of animal physiology throughout life. In addition to regulating metabolism and growth, insulin–IGF receptor signalling has recently been linked to a variety of new, cell type-specific functions. In the last century, key questions have focused on how structural differences of insulin and IGFs affect receptor activation, and how insulin–IGF receptor signalling translates into pleiotropic biological functions. Technological advances such as cryo-electron microscopy have provided a detailed understanding of how native and engineered ligands activate insulin–IGF receptors. In this Review, we highlight recent structural and functional insights into the activation of insulin–IGF receptors, and summarize new agonists and antagonists developed for intervening in the activation of insulin–IGF receptor signalling. Furthermore, we discuss recently identified regulatory mechanisms beyond ligand–receptor interactions and functions of insulin–IGF receptor signalling in diseases.</p>