Models with two Higgs doublets, offer a rich framework to address various theoretical problems Beyond the Standard Model (BSM), ranging from the hierarchy problem (in SUSY), to providing a successful Electroweak baryogenesis, or even to provide dark matter candidates (in inert versions). In this talk I will focus on the strong phenomenological constraints already imposed on the parameter space of the softly broken Z2 symmetric two higgs doublet models (commonly known as 2HDMs). I will discuss the prospects for probing sign changes in the couplings of the model (relative to the SM) in the loop induced Higgs-gluon-gluon and Higss-photon-photon effective vertices at the next LHC run. I will present dense parameter space scans with the ScannerS tool which include all known theoretical and phenomenological constraints, and will find that, with all 8 TeV data analysed, all wrong sign scenarios are allowed in all Yukawa types, even at the 1sigma level. Finally I will present a scenario where the alignment limit could be excluded due to non-decoupling in the case where the heavy CP-even Higgs is the one discovered at the LHC.