While the Standard Model (SM) of particle physics presents a complete and well-tested theory, there remain important pieces missing from our understanding of high energy physics. Two of the most promising sectors in which to search for beyond the SM (BSM) physics are the Higgs and neutrino sectors, which are the two least well-understood of the Standard Model. In this work, we examine these two sectors and their interplay with BSM models through the lens of experimental evidence. We begin with an examination of the Large Hadron Collider (LHC) Higgs, which appears so far to be SM-like, in a number of contexts. We first examine the indirect constraints one may impose on light Higgs Yukawa couplings given existing rate measurements from the ATLAS and CMS experiments. We then move to an examination of low energy minimal supersymmetric models, focusing on an inversion of the bottom Yukawa and its phenomenological consequences. Finally, we analyze a high-energy theory in which one may dynamically obtain alignment of the physical and SM-like Higgs states. The results of these studies illustrate that there are a number of ways in which new physics may still manifest in the Higgs sector. We then move to an examination of new physics searches in the neutrino sector, focusing on the impact of neutrino-nucleus cross section modeling on new physics signals in neutrino accelerator experiments. While neutrino experiments provide a rich environment to study BSM physics, we find that cross section uncertainties limit our sensitivity to new physics. Finally, we end with an analysis of theoretical bounds on two Higgs doublet models (2HDM), with an application of these bounds on the phenomenology of general 2HDMs.