[en] Possible models of Yukawa interaction are discussed in the two Higgs doublet model (THDM) under the discrete symmetry imposed to avoid the flavor changing neutral current at the leading order. It is known that there are four types of such models corresponding to the possible different assignment of charges for the discrete symmetry on quarks and leptons. We first examine decay properties of Higgs bosons in each type of the models, and summarize constraints on the models from current experimental data. We then shed light on the differences among these models in collider phenomenology. In particular, we mainly discuss so-called the Type-II THDM and the Type-X THDM. The Type-II THDM corresponds to the model with the same Yukawa interaction as the minimal supersymmetric standard model (MSSM). On the other hand, in the Type-X THDM, additional Higgs bosons can predominantly decay into leptons. This scenario may be interesting because of the motivation for a light charged Higgs boson scenario such as in the TeV scale model of neutrino, dark matter and baryogenesis. We study how we can distinguish the Type-X THDM from the MSSM at the Large Hadron Collider and the International Linear Collider. (author)