Recently the ATLAS Collaboration carried out two searches for the Standard Model four-top-quark production in the single-lepton and opposite-sign dilepton channel, and in the same-sign dilepton and multilepton channels. The searches are based on $pp$ collision data with a center-of-mass energy $\sqrt{s} = 13$ TeV collected by the ATLAS detector at the Large Hadron Collider during the year 2015 and 2016, corresponding to an integrated luminosity of $36.1$ fb$^{-1}$. No significant excess above the Standard Model expectation is observed in both searches. The results are combined and an observed (expected) upper limit of 49 fb (19 fb), or 5.3 (2.1) times the four-top-quark Standard Model cross section is obtained at 95% confidence level.