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.Comment: 44 pages, accepted by to Review of Modern Physic