The ALICE muon spectrometer studies the production of quarkonia and open heavy- flavour particles. It is equipped with a Trigger System composed of Resistive Plate Chambers which, by applying a transverse-momentum-based muon selection, minimises the background from light-hadron decays. The system has been continuously taking data throughout the LHC Run I; it has undergone maintenance and consolidation operations during the LHC shutdown period 1. In the first year of the LHC Run II, the system, fully recommissioned, has participated in data taking in pp and Pb/en-dashPb collisions. The performance of the system throughout the last data-taking period is presented.