Abstract A measurement of fiducial and differential cross-sections for $$W^+W^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>W</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>W</mml:mi><mml:mo>-</mml:mo></mml:msup></mml:mrow></mml:math> production in proton–proton collisions at $$\sqrt{s}=13$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>13</mml:mn></mml:mrow></mml:math> TeV with the ATLAS experiment at the Large Hadron Collider using data corresponding to an integrated luminosity of 36.1 $$\hbox {fb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>fb</mml:mtext><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> is presented. Events with one electron and one muon are selected, corresponding to the decay of the diboson system as $$WW\rightarrow e^{\pm }\nu \mu ^{\mp }\nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>W</mml:mi><mml:mi>W</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mi>ν</mml:mi><mml:msup><mml:mi>μ</mml:mi><mml:mo>∓</mml:mo></mml:msup><mml:mi>ν</mml:mi></mml:mrow></mml:math> . 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.