  We analyze the Two-Higgs-Doublet Models (2HDMs) of Type I and II for
consistency with the latest measurements of the ~125.5 GeV Higgs-like signal at
the LHC. To this end, we perform scans of the 2HDM parameter space taking into
account all relevant pre-LHC constraints as well as the most recent limits
coming from searches for heavy Higgs-like states at the LHC. The current status
of the 2HDMs of Type I and II is discussed assuming that the observed 125.5 GeV
state is one of the two CP-even Higgs bosons, either the lighter h or the
heavier H. Implications for future experiments, including expectations
regarding other lighter or heavier Higgs bosons are given. The possible
importance of heavier Higgs bosons feeding the signals for the 125.5 GeV state
is also evaluated.
