The LHC produces a vast sample of top quark pairs and single top
quarks. Measurements of the inclusive top quark production cross-sections at
the LHC have reached a precision of several percent, and test state-of-the-art
QCD predictions. This review describes several recent ATLAS top-pair
cross-section measurements at different centre-of-mass energies, as well
as a recent combination of Run~1 measurements from both ATLAS and CMS, and
the latest ATLAS s-channel single top production result with the full
Run~2 data sample.