The PHENIX Muon Spectrometer consists of two central arms and two muon arms. Each muon arm consists of a tracking system, which measures the momentum vector of each muon, together with a muon identifier, which separates muons from other particles and provides the muon trigger for PHENIX. Los Alamos technical staff led the design, construction, and operation of the muon tracking system over a period of more than ten years. Staff from Oak Ridge National Laboratory led the muon identification system effort. Los Alamos also pioneered the use of cathode-strip-chamber technology for the high-precision tracking chambers used to accurately measure the muon trajectories and momentum.