The International Linear Collider Technical Design Report (TDR) describes in four volumes the physics case and the design of a 500 GeV centre-of-mass energy linear electron-positron collider based on superconducting radio-frequency technology using Niobium cavities as the accelerating structures. The accelerator can be extended to 1 TeV and also run as a Higgs factory at around 250 GeV and on the Z0 pole. A comprehensive value estimate of the accelerator is give, together with associated uncertainties. It is shown that no significant technical issues remain to be solved. Once a site is selected and the necessary site-dependent engineering is carried out, construction can begin immediately. The TDR also gives baseline documentation for two high-performance detectors that can share the ILC luminosity by being moved into and out of the beam line in a "push-pull" configuration. These detectors, ILD and SiD, are described in detail. They form the basis for a world-class experimental programme that promises to increase significantly our understanding of the fundamental processes that govern the evolution of the Universe.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

The original online version of this article was revised: The additional reference [139] has been added. Tao Han’s ORICD ID has been incorrectly assigned to Chengcheng Han and Chengcheng Han’s ORCID ID to Tao Han. Yang Ma’s ORCID ID has been incorrectly assigned to Lianliang Ma, and Lianliang Ma’s ORCID ID to Yang Ma. The original article has been corrected.