The ATLAS tile calorimeter (TileCal) is the hadronic sampling calorimeter covering the central region of the ATLAS detector at the Large Hadron Collider (LHC). This paper gives an overview of the calorimeter’s operation and performance during the years 2015–2018 (Run 2). In this period, ATLAS collected proton–proton collision data at a centre-of-mass energy of 13 TeV and the TileCal was 99.65% efficient for data-taking. The signal reconstruction, the calibration procedures, and the detector operational status are presented. The performance of two ATLAS trigger systems making use of TileCal information, the minimum-bias trigger scintillators and the tile muon trigger, is discussed. Studies of radiation effects allow the degradation of the output signals at the end of the LHC and HL-LHC operations to be estimated. Finally, the TileCal response to isolated muons, hadrons and jets from proton–proton collisions is presented. The energy and time calibration methods performed excellently, resulting in good stability and uniformity of the calorimeter response during Run 2. The setting of the energy scale was performed with an uncertainty of 2%. The results demonstrate that the performance is in accordance with specifications defined in the Technical Design Report.