We compare the predictions of six models for neutrino (and antineutrino) production of trimuon events. In particular, results are given for models based on heavy-charged-lepton decays, heavy-neutral- lepton decays together with heavy-quark decays, diffractive production and decay of heavy-quark pairs, heavy-quark cascade decays, the decays of Higgs mesons, and the radiative production of muon pairs. Our comparison should help to unravel the sources of the trimuon events detected at Fermilab and CERN. We also examine the probability of explaining the so-called superevents in which the muons are extremely energetic.