In this thesis I explore a collection of disparate approaches in the search for new physics beyond the Standard Model (BSM). The research here focuses on the potentially interesting signals that BSM physics could produce; the result is a combination of model building, cosmology, collider physics, and gravitational waves. The signals of the new physics are determined and used to discuss both the discovery potential of next-generation experiments and the parameter space bounds from current collaborations. There are three projects that make up the core of the research presented here. The first of these explores the possibility of detecting gravitational waves generated by first-order phase transitions in multiple dark sectors. The cosmological history of this framework is outlined and the gravitational wave profiles are generated. These profiles are checked against projections of next-generation gravitational wave experiments, demonstrating that multiple hidden sectors can indeed produce unique gravitational wave signatures that will be probed by these future experiments. Next up is a study of one of the simplest extensions to the SM: a light Higgs portal scalar. Such a particle could be abundantly produced in the earth's atmosphere and decay in large-volume neutrino detectors. I point out that the Hyper Kamiokande detector bears a strong discovery potential of probing such particles in an uncharted parameter space that is explored by intensity frontier experiments including rare kaon decays. This search can be generalized to other new light states and is highly complementary to beam experiments. Finally, I explore models of new physics that can give rise to large enhancements to the rate of Higgs decay to Z-gamma while still being consistent with other measurements. I show that this is impossible in simple models with one additional multiplet, and also in well motivated models such as the MSSM and folded SUSY. I do find models with several multiplets that carry electroweak charge where such an enhancement is possible, but they require destructive interference effects. I also show that kinematic measurements in Higgs decay to four leptons can be sensitive to such models. Finally, I explore the sensitivity of four lepton measurements to supersymmetric models.