  In two Higgs doublet models (2HDM), there exists an interesting possibility,
the hidden light Higgs scenario, that the discovered SM-like Higgs boson is the
heavier \textit{CP}-even Higgs boson $H^0$ and the lighter \textit{CP}-even
$h^0$ has not been observed yet in any experiment. We study the current status
of this scenario in Types I, II, X, and Y, through the scans of the 2HDM
parameters with all relevant theoretical and experimental constraints. We
employ not only the most up-to-date Higgs signal strength measurements with the
feed-down effects, but also all the available LHC exclusion limits from heavy
Higgs searches. Adjusting the heavier $H^0$ to the 125 GeV state while hiding
the lighter $h^0$ from the LEP Higgs search prohibits the extreme decoupling
limit: there exist upper bounds on the masses of the pseudoscalar $A^0$ and the
charged Higgs $H^\pm$ below about 600 GeV. In addition, the $Z_2$ symmetry is
shown to be a good approximate symmetry since the soft $Z_2$ symmetry breaking
parameter $m_{12}^2$ should be less than about (45 GeV)$^2$. Most
interestingly, a few parameters in the Higgs potential and the related Higgs
triple and quartic couplings are shown to be meaningfully constrained by the
current data. The double Higgs-strahlung process at an $e^+ e^-$ collider is
also studied.
