Abstract The muon spectrometer of the ATLAS detector will be significantly upgraded during the Phase-II upgrade in Long Shutdown 3 in order to cope with the operational conditions at the High-Luminosity LHC in Run 4 and beyond. Most of the electronics for the Resistive Plate Chambers (RPC), Thin Gap Chambers (TGC), and Monitored Drift Tube (MDT) chambers will be replaced to make them compatible with the higher trigger rates and longer latencies necessary for the new level-0 trigger. The MDT chambers will be integrated into the level-0 trigger in order to sharpen the momentum threshold. Additional RPC chambers will be installed in the inner barrel layer to increase the acceptance and robustness of the trigger. Some of the MDT chambers in the inner barrel layer will be replaced with new small-diameter MDTs. New TGC triplet chambers in the barrel–endcap transition region will replace the current TGC doublets to suppress the high trigger rate from random coincidences in this region. The power system for the RPC, TGC, and MDT chambers and electronics will need to be replaced due to component obsolescence, aging, and radiation damage. A high- η tagger is under consideration to extend the angular acceptance for muon identification. The Phase-II upgrade concludes the process of adapting the muon spectrometer to the ever increasing performance of the LHC, which started with the Phase-I upgrade New Small Wheel project that will replace the Cathode Strip Chambers and the MDT chambers of the innermost endcap wheels by Micromegas and small-strip TGCs.