Constraints on and future prospects for two-Higgs-doublet models in light of the LHC Higgs signal

We analyze the two-Higgs-doublet models (2HDMs) of Type I and Type II for consistency with the latest measurements of the similar to 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 Type 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.