  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 Higgs boson, and
heavier CP-even and charged Higgs 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, $B$ physics
observables like $b\to s \gamma$ as well as the 125 GeV Higgs boson properties
measured at the LHC.
