Accelerators in the 21st Century

More than 30,000 accelerators are in operation worldwide. Of these less than 1% are devoted to basic research. Prominent among the latter are high-energy particle colliders - powerful engines of discovery and precision measurement, which have played an essential role in establishing the standard model of particle physics. Technological innovation has allowed building colliders for ever higher energy and better performance, at decreasing specific cost. New concepts will allow reaching even higher luminosities and energies throughout the coming century. One cost-effective strategy for future collider implementation is staging. For example, a future circular collider could first provide electron-positron collisions, then hadron collisions (proton-proton and heavy-ion), and, finally, the collision of muons. Indeed, cooling-free muon colliders, realizable in a number of ways, promise an attractive and energy-efficient path towards lepton collisions at tens of TeV. While plasma accelerators and dielectric accelerators offer unprecedented gradients, the construction of a high-energy collider based on these advanced technologies still faces a number of challenges. Pushing the accelerating gradients or bending fields ever further, the breakdown of the QED vacuum may, or may not, set an ultimate limit to electromagnetic acceleration.