Strong electron-electron and electron-phonon correlations are responsible for important effects in materials such as magnetism and superconductivity, leading to a broad spectrum of uses in quantum information, clean energy, catalysis, and much more. Materials characterization, discovery, and design have been made highly efficient through computational approaches which can circumvent time-consuming experiments; however most such approaches suffer from the "exponential-scaling wall" of performing calculations on correlated electrons, where accuracy and computational tractability cannot simultaneously be achieved. In this dissertation, two novel approaches are introduced: one for affordably treating solid-state point defects in an ab-initio software using the full toolbox of post-Hartree Fock methods, and another for casting the complicated electron-phonon physics of, for example, conventional superconductors into the simple language of chemical bonding. Applications of these approaches are presented in the context of defect-based quantum information and two cases of superconductivity prediction.