  Updating various theoretical and experimental constraints on the four
different types of two-Higgs-doublet models (2HDMs), we find that only the
``lepton-specific" (or ``type X") 2HDM can explain the present muon g$-$2
anomaly in the parameter region of large $\tan\beta$, a light CP-odd boson, and
heavier CP-even and charged bosons which are almost degenerate. The severe
constraints on the models come mainly from the consideration of vacuum
stability and perturbativity, the electroweak precision data, the $b$-quark
observables like $B_S \to \mu\mu$, the precision measurements of the lepton
universality as well as the 125 GeV boson property observed at the LHC.
