An overview of the most recent single-top-quark cross section results carried out by the ATLAS and CMS experiments of the CERN LHC is presented in this document. The latest t-channel and tW production cross section results at 13 TeV are shown together with the ATLAS and CMS single-top-quark cross section combinations at 7 and 8 TeV. The observation of the associated production of a top quark and a Z boson at 13 TeV is also presented. All measurements are consistent with the SM predictions. These results demonstrate a good understanding of the electroweak production mechanism of single-top-quarks providing important constraints on interference models and better understanding of the structure of the proton. More data and higher production cross sections at the LHC allow us to probe differentially the single-top-quark processes; some differential cross section measurements are already performed and discussed here as well.