The Time Projection Chamber is the main tracking and particle identification detector of the ALICE experiment. The high luminosities delivered by the CERN LHC in Run 2 (2015-2018) posed new challenges in terms of detector performance and efficiency. The hardware components and calibration software were optimized and further developed to meet those challenges and maximize the quality of the data. In addition, unexpectedly large local distortions of the drift paths of ionization electrons have been observed at the edges of specific readout chambers. These distortions are caused by ions which originate at the readout chambers, leading to local space-charge accumulation in the drift volume of the TPC. A new calibration procedure has been developed to correct for the space-charge distortions. Extensive studies have been performed to understand the origin of the space charge as well as to find a way to effectively mitigate the effect. For Run 3 starting in 2021, the new readout chambers of the upgraded TPC will be based on Gas Electron Multipliers. This implies an intrinsic backflow of ions which leads to large space-charge distortions in most of the TPC drift volume at the highest luminosities. The simulation and calibration of the space-charge effect are a major part of the new detector software framework.