Limiting two-Higgs-doublet models

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.