This paper provides a review of the experimental studies of processes with a single top quark at the Tevatron proton-antiproton collider and the LHC proton-proton collider. Single top-quark production in the t-channel process has been measured at both colliders. The s-channel process has been observed at the Tevatron, and its rate has been also measured at the center-of-mass energy of 8 TeV at the LHC in spite of the comparatively harsher background contamination. LHC data also brought the observation of the associated production of a single top quark with a W boson as well as with a Z boson. The Cabibbo-Kobayashi-Maskawa matrix element |Vtb| is extracted from the single-top-quark production cross sections, and t-channel events are used to measure several properties of the top quark and set constraints on models of physics beyond the Standard Model. Rare final states with a single top quark are searched for, as enhancements in their production rates, if observed, would be clear signs of new physics.
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