This thesis describes work on several research topics in which transport and spectroscopy are influenced by strong electron-nuclear or nuclear-nuclear interactions. First, I give a broad overview of the motivations and background for the main topics covered in this thesis. In the next section, I explore the applicability of perturbative quantum master equations to linear absorption and nonlinear two-dimensional and pump-probe spectroscopies. Next, I introduce a theory of charge transport in

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... nic semiconductors that unifies two popular pictures: incoherent polaron hopping and transient localization due to dynamic disorder. In the next section, I investigate the impact of phonon anharmonicity on the charge transport dynamics of soft semiconductors. Finally, I present a new method of efficiently calculating anharmonic vibrational spectra from ab initio molecular potential energy surfaces.