With increasing instantaneous luminosity at the LHC come additional reconstruction challenges. At high luminosity, many collisions occur simultaneously within one proton-proton bunch crossing. The isolation of an interesting collision from the additional "pileup" collisions is needed for effective physics performance. In the CMS Collaboration, several techniques capable of mitigating the impact of these pileup collisions have been developed. Such methods include charged-hadron subtraction, pileup jet identification, isospin-based neutral particle "$\delta\beta$" correction, and, most recently, pileup per particle identification. This paper surveys the performance of these techniques for jet and missing transverse momentum reconstruction, as well as muon isolation. The analysis makes use of data corresponding to 35.9 fb$^{-1}$ collected with the CMS experiment in 2016 at a center-of-mass energy of 13 TeV. The performance of each algorithm is discussed for up to 70 simultaneous collisions per bunch crossing. Significant improvements are found in the identification of pileup jets, the jet energy, mass, and angular resolution, missing transverse momentum resolution, and muon isolation when using pileup per particle identification.