Abstract. At present, particle physics faces problems related with disparity in diphoton decay of Higgs boson, discrepancy between theory and experiment of about 3.6σ in anomalous magnetic moment of the muon and neutrino physics. Moreover, the existence of Dark Matter and the Matter-Antimatter Asymmetry are challenges for any physical model. In this review I present some solutions in the framework of the 3-3-1 models. The simple (by Higgs sector) models contain the hybrid inflationary scenario and the first-order phase transitions, from which leptogenesis needed for BAU is followed. By these considerations, some bounds on model parameters are derived.Keywords: particle-theory and field-theory models of the early Universe, supersymmetric models, non-standard-model neutrinos, right-handed neutrinos.