The ATLAS experiment is designed to study the proton-proton (pp) collisions produced at the Large Hadron Collider (LHC) at CERN. Liquid argon (LAr) sampling calorimeters are used for all electromagnetic calorimetry in the pseudo-rapidity region |η| < 3.2, as well as for hadronic calorimetry in the range 1.5 < |η| < 4.9. The electromagnetic calorimeters use lead as passive material and are characterized by an accordion geometry that allows a fast and uniform response without azimuthal gaps. Copper and tungsten were chosen as passive material for the hadronic calorimetry; while a classic parallel-plate geometry was adopted at large polar angles, an innovative design based on cylindrical electrodes with thin liquid argon gaps is employed at low angles, where the particle flux is higher. All detectors are housed in three cryostats maintained at about 88.5 K. The 182,468 cells are read out via front-end boards housed in on-detector crates that also contain monitoring, calibration, trigger and timing boards. In the first three years of LHC operation, approximately 27 fb−1 of pp collision data were collected at centre-of-mass energies of 7-8 TeV. Throughout this period, the calorimeter consistently operated with performances very close to specifications, with high data-taking efficiency. This is in large part due to a sophisticated data monitoring procedure designed to quickly identify issues that would degrade the detector performance, to ensure that only the best quality data are used for physics analysis. After a description of the detector design, main characteristics and operation principles, this paper details the data quality assessment procedures developed during the 2011 and 2012 LHC data-taking periods, when more than 98% of the luminosity recorded by ATLAS had high quality LAr calorimeter data suitable for physics analysis.