We will review single top-quark production cross section measurements in proton-proton collisions based on the 8 TeV and 13 TeV data collected by ATLAS and CMS detectors. For the production of single top-quarks and single anti-top-quarks through t-channel, we will present the fiducial and total production cross sections, their ratio and differential cross-sections. Measurements of the inclusive, differential production cross section of a single top quark in association with a W boson, will be presented. In addition, we will present the interference effects between top-quark pair production and associated production of a single top quark with W boson. Finally we will present rare single top quark measurements in the s-channel and the production with the association to the Z boson or photon.