  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.
