Updating various theoretical and experimental constraints
on the four different types of two Higgs doublet models,
we find only the lepton-specific or type-X 2HDM can explain
the muon g-2 anomaly in the parameter region of large tanbeta, a light CP-odd
Higgs boson, and almost degenerate heavier CP-even and charged Higgs bosons.
We also discuss tau-rich signatures at the LHC to test the relevant model parameter space.
