There must exist physics beyond the Standard Model, but we do not yet know what form it takes. Six years ago we began exploring the microscopic world from a completely new perspective, through the Higgs physics, and many theorists believe that the New Physics will first manifest itself via non-minimal Higgs sector. Multi-Higgs-doublet models represent a very popular class of such models with rich observable consequences. For several decades, the two-Higgs-doublet model proposed by T.D.Lee in 1973 was the main playground, but recently the community look beyond two doublets. In this talk I will present a brief overview of this research activity and show, as an illustration, a particularly curious three-Higgs-doublet model based on CP symmetry of order 4 together with its phenomenological consequences.
