The CMS Collaboration has developed new sets of parameters ("tunes") for the underlying-event (UE) modeling of the PYTHIA8, PYTHIA6, and HERWIG++ Monte Carlo (MC) event generators using different parton distribution functions (PDFs). These tunes are constructed by fitting CMS UE proton-proton (pp) data at √s = 7 TeV and CDF UE proton-antiproton (pp) data at lower √s to study UE models and constrain their parameters, improving predictions for 13 TeV pp collisions. The tunes are validated by comparing them to "minimum bias" (MB) events, multijet, and Drell–Yan (q̅ → Z/γ* → lepton-antilepton+jets) observables at 7 and 8 TeV, as well as predictions for MB and UE observables at 13 TeV. The tunes are also compared to CMS DPS tunes, which are determined by fitting observables sensitive to double-parton scattering (DPS) processes. The CMS UE tunes are shown to describe UE data well, with improved accuracy compared to previous tunes, and can be interfaced to higher-order matrix element (ME) generators without additional tuning of MPI parameters. The CMS UE tunes provide a better description of MB observables and Drell–Yan observables compared to previous tunes, and are consistent with the values determined from fitting DPS-sensitive observables.The CMS Collaboration has developed new sets of parameters ("tunes") for the underlying-event (UE) modeling of the PYTHIA8, PYTHIA6, and HERWIG++ Monte Carlo (MC) event generators using different parton distribution functions (PDFs). These tunes are constructed by fitting CMS UE proton-proton (pp) data at √s = 7 TeV and CDF UE proton-antiproton (pp) data at lower √s to study UE models and constrain their parameters, improving predictions for 13 TeV pp collisions. The tunes are validated by comparing them to "minimum bias" (MB) events, multijet, and Drell–Yan (q̅ → Z/γ* → lepton-antilepton+jets) observables at 7 and 8 TeV, as well as predictions for MB and UE observables at 13 TeV. The tunes are also compared to CMS DPS tunes, which are determined by fitting observables sensitive to double-parton scattering (DPS) processes. The CMS UE tunes are shown to describe UE data well, with improved accuracy compared to previous tunes, and can be interfaced to higher-order matrix element (ME) generators without additional tuning of MPI parameters. The CMS UE tunes provide a better description of MB observables and Drell–Yan observables compared to previous tunes, and are consistent with the values determined from fitting DPS-sensitive observables.