Abstract: The theory of superconductivity is magnificently broad and deep, and different theoretical tools are needed depending on the nature of the problem of interest. In this talk I will introduce two commonly used approaches and exemplify them through two completed projects. The first project uses numerical exact determinant Quantum Monte Carlo methods to investigates the extent of which proximity to Van Hove Singularities increases the superconducting transition temperature. The second project starts from phenomenological time-dependent Ginzburg–Landau theory and explores how NV centers can be used as experimental probes of nonlocal superconducting fluctuations, accessing information beyond conventional local AC measurements