In the first part of the thesis, the need for physics beyond the Standard Model, as attested to by the evidence of dark matter, motivates us to study the effects of introducing into the standard theory of Leptogenesis a hidden sector scalar coupled to the Standard Model through the Higgs portal. We find that the new interactions are not constrained by the Davidson-Ibarra bound, thus allowing us to lower the mass scale of Leptogenesis into the TeV range, accessible to experiments. We then consider a broader class of new physics models below the electroweak scale, and classify precision observables according to whether or not deviations from the Standard Model at current levels of sensitivity can be explained purely in terms of new light degrees of freedom. We find that hadronic precision observables, e.g. those that test fundamental symmetries such as electric dipole moments, are unambiguous pointers to new UV physics. In the second part of the thesis, motivated by recent measurements of the spatial structure of impurities embedded in superconductors (SC), we study the effect of superconductivity on impurity states by generalizing the Anderson model of a quantum s-wave impurity to include orbital degeneracy. We find that the proximity effect induces an electron-electron attractive potential on the impurity site that mirrors the BCS pairing mechanism, resulting in the appearance of atomic Cooper pairs within the superconducting energy gap, called Yu-Shiba-Rusinov (YSR) states. We find that electron orbital degeneracy allows YSR states to have non-trivial orbital quantum numbers thus opening the possibility for optical transitions among YSR states. We enumerate the one-photon selection rules that apply to YSR states, unveiling transitions to the vacuum state that are forbidden in the normal state. / Graduate