During Run 2 (covering 2015-2018) the LHC achieved instantaneous luminosities as high as 2x$10^{34}$cm$^2$s$^{-1}$ while delivering proton-proton collisions at $\sqrt{s}=13$ TeV. The challenge for the trigger system of the CMS experiment is to reduce the registered event rate from about 40 MHz to about 1 kHz. In this poster, muon reconstruction and identification algorithms used during Run 2 and their improvements are presented. The new algorithms maintain the acceptance of the muon triggers at the same or even lower rate throughout the data-taking period despite the increasing number of additional proton-proton interactions in each LHC bunch crossing. We will focus on the single and double muon triggers with the lowest sustainable transverse momentum thresholds used by CMS. The efficiency is measured in a transverse momentum range from 8 to several hundred GeV.