Muon triggers are essential for studying a variety of physics processes in the ATLAS experiment at the LHC, including Standard Model measurements and searches for new physics. The ATLAS muon trigger system consists of a hardware-based Level-1 trigger and a software-based High-Level Trigger for reconstruction purposes. The muon triggers have been optimized during Run 2 to provide high efficiencies while keeping the trigger rate low. These proceedings give an overview of how ATLAS triggers on muons, recent improvements to the trigger system, the performance of the muon trigger based on Run 2 data, and the upgrades underway for Run 3.