The CMS muon system has played a key role for many physics results obtained from the LHC Run1 and Run2 data. During the Long Shutdown (2013-2014), as well as during the last year-end technical stop (2015-2016), significant consolidation and upgrades have been carried out on the muon detectors and on the Level-1 (L1) muon trigger. The algorithms for muon reconstruction and identification have also been improved for both the High-Level Trigger (HLT) and the offline reconstruction. Results of the performance of muon detectors, reconstruction and trigger, obtained using data collected at 13 TeV center-of-mass energy during the 2015 and 2016 LHC runs, are presented. Comparison of simulation with experimental data is also discussed where relevant. The system's state of the art is also shown, as well the improvements foreseen to achieve excellent overall quality of muon reconstruction in the high-luminosity conditions expected during Run2.