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Abstract Particle physics has arrived at an important moment of its history. The discovery of the Higgs boson has completed the Standard Model, the core theory behind the known set of elementary particles and fundamental interactions. However, the Standard Model leaves important questions unanswered, such as the nature of dark matter, the origin of the matter–antimatter asymmetry in the Universe, and the existence and hierarchy of neutrino masses. To address these questions and the origin of the newly discovered Higgs boson, high-energy colliders are required. Future generations of such machines must be versatile, as broad and powerful as possible with a capacity of unprecedented precision, sensitivity and energy reach. Here, we argue that the Future Circular Colliders offer unique opportunities, and discuss their physics motivation, key measurements, accelerator strategy, research and development status, and technical challenges. The Future Circular Collider integrated programme foresees operation in two stages: initially an electron–positron collider serving as a Higgs and electroweak factory running at different centre-of-mass energies, followed by a proton–proton collider at a collision energy of 100 TeV. The interplay between measurements at the two collider stages underscores the synergy of their physics potentials.