My PhD research focuses on exotic Higgs physics. The Higgs boson is the second heaviest observed particle and the latest one to have been discovered. Its first observation at the Large Hadron Collider five years ago was welcomed as great news for many physicists. It was the final confirmation of the Brout-Englert-Higgs mechanism explaining the mass of the other elementary particles that was established more than 50 years ago. However few other physicists were quite disappointed by this discovery. The reason is simple: up to now everything acts as predicted by the main currently accepted theory in particle physics, the Standard Model. Nonetheless even if a lot of its predictions are indeed realized in Nature, there remain unexplained phenomena and small problems inside the theory which call for new physics models. During my PhD I studied several processes in one of these exotic models called the Two-Higgs-Doublet Model in which, instead of having only one Higgs boson, there are five distinct ones. I reviewed three main Higgs boson production modes involving loops at the lowest order in perturbation theory. Given the lack of automated events generation tools for this kind of diagrams in the past, I implemented a reweighting technique to overcome these limitations and to reduce the uncertainty on theoretical predictions by a factor of two. This precision improvement is of vital importance when comparing with experimental data. Finally I put constraints on the top Yukawa couplings in a generic model and I studied its consequences in a simplified Dark Matter model along with other cosmological and collider constraints.