  The discovery of the 125 GeV Higgs boson and the measurement of its branching
ratios has initiated the exploration of the electroweak symmetry breaking
sector. There have been numerous studies exploring the restrictions these
results place on the parameter space of two Higgs doublet models. We extend
these results to include the full data set and study the expected sensitivity
that can be obtained with 300 and 3000 inverse femtobarn of integrated
luminosity. In addition, searches for a heavy Standard Model Higgs boson are
also considered. It is shown that the nonobservation of such a Higgs boson can
substantially narrow the allowed regions of parameter space in two Higgs
doublet models. Finally, projections for the ILC at the center of mass energy
250, 500, and 1000 GeV are investigated.
