The mechanistic target of rapamycin complex 1 (mTORC1) controls cell growth and metabolism in response to nutrients, energy levels, and growth factors. It contains the atypical kinase mTOR and the RAPTOR subunit that binds to the Tor signalling sequence (TOS) motif of substrates and regulators. mTORC1 is activated by the small GTPase RHEB (Ras homologue enriched in brain) and inhibited by PRAS40. Here we present the 3.0 ångström cryo-electron microscopy structure of mTORC1 and the 3.4 ångström structure of activated RHEB–mTORC1. RHEB binds to mTOR distally from the kinase active site, yet causes a global conformational change that allosterically realigns active-site residues, accelerating catalysis. Cancer-associated hyperactivating mutations map to structural elements that maintain the inactive state, and we provide biochemical evidence that they mimic RHEB relieving auto-inhibition. We also present crystal structures of RAPTOR–TOS motif complexes that define the determinants of TOS recognition, of an mTOR FKBP12–rapamycin-binding (FRB) domain–substrate complex that establishes a second substrate-recruitment mechanism, and of a truncated mTOR–PRAS40 complex that reveals PRAS40 inhibits both substrate-recruitment sites. These findings help explain how mTORC1 selects its substrates, how its kinase activity is controlled, and how it is activated by cancer-associated mutations. The cryo-electron microscopy and crystal structures of several mTORC1 complexes, and accompanying biochemical analyses, shed light on how mTORC1 is regulated and how cancer mutations lead to its hyperactivation. Mechanistic target of rapamycin complex 1 (mTORC1) is a protein complex that is important for regulating cell growth and homeostasis and is aberrantly regulated in many diseases such as cancer, diabetes and neurodegeneration. Here, Nikola Pavletich and colleagues use cryo-electron microscopy and crystallography to determine the structures of several mTORC1 complexes. The structures and accompanying biochemical analysis provide mechanistic insights into how mTORC1 is allosterically activated by the GTPase RHEB, how it is inhibited by PRAS40, and how it recognizes substrates via the TOS motif. The findings also shed light on how cancer mutations lead to hyperactivation of mTORC1.