A measurement of fiducial and differential cross-sections for W+W- production in proton–proton collisions at s=13 TeV with the ATLAS experiment at the Large Hadron Collider using data corresponding to an integrated luminosity of 36.1 fb - 1 is presented. Events with one electron and one muon are selected, corresponding to the decay of the diboson system as WW→ e±νμ∓ν. To suppress top-quark background, events containing jets with a transverse momentum exceeding 35 GeV are not included in the measurement phase space. The fiducial cross-section, six differential distributions and the cross-section as a function of the jet-veto transverse momentum threshold are measured and compared with several theoretical predictions. Constraints on anomalous electroweak gauge boson self-interactions are also presented in the framework of a dimension-six effective field theory. © 2019, CERN for the benefit of the ATLAS collaboration.