As our ability to probe the nature of the fundamental particles and their interactions improves with increasing particle collider data, we have more compelling reasons to explore models beyond the Standard Model (SM). Searches for new Higgs bosons of an extended Higgs sector beyond the SM at the Large Hadron Collider (LHC) can be interpreted in the framework of the two-Higgs-doublet model (2HDM). 2HDMs are among the simplest extensions extensions of the SM that yield interesting phenomenology. Understanding the pattern in which Higgs bosons couple to fermions is important for searches for Higgs bosons beyond the SM (BSM) and flavor physics. In this dissertation, we study two specific patterns of Yukawa couplings which are designed to provide a more general Yukawa framework than the common Z2-symmetric models, providing access to more 2HDM parameter space, while still controlling the potentially dangerous flavor changing neutral currents (FCNCs).

The first project presented demonstrates that Z2-symmetric models are too restrictive and experimentalists should not limit themselves to these specialized models. Instead, we should allow experiments to determine the nature of Yukawa couplings.In this work, we assume the Yukawa coupling matrices are flavor-diagonal and so proportional to the mass matrices. This model is known as the flavor-aligned 2HDM (A2HDM), of which Z2-symmetric models are a subset. To demonstrate this paradigm shift, we devised two scenarios in which we simultaneously fit two excesses for BSM scalars in LHC data within the A2HDM via parameter scans. We then present a few benchmark parameter points of interest to demonstrate what channels may reveal more information in future BSM Higgs boson searches.

In the second project, we work under the assumption that the 2HDM Yukawa matrices are of the four-texture form, with zeros in particular entries, and the parameters therein have a hierarchy in accordance with the fermion masses. This structure is motivated by the Cheng-Sher-like physical Yukawa couplings that it can produce, which enables small flavor-violating processes occur but systematically avoids current limits on FCNCs. We show that these models are phenomenologically viable and recast the calculation of the physical Yukawa couplings in a basis-independent formulation by rotating into the Higgs basis before assuming a particular structure for the Yukawa coupling matrices. Finally, we discuss the landscape of flavor-violating observables' predictions in this model, the landscape of their measurements, and the prospect of these channels to be measured at future high-energy particle colliders.