For nearly a century, the Born-Oppenheimer (BO) framework has served as the foundation of theoretical and computational chemistry. Chemists routinely perform electronic structure calculations and construct potential energy surfaces $E_{\rm BO} (\bm R)$ as functions of nuclear position $\bm R$, and then propagate molecular dynamics on one or more of those same potential energy surfaces. However, despite the vast amount of chemical intuition has been built on the BO framework, dynamics along BO potential surfaces completely ignore linear and angular momentum transfer between nuclei and electrons and even fails to conserve total linear and angular momentum in certain scenarios (e.g., when propagating on a single symmetry broken surface). In this thesis, we begin by highlighting the existing problems of adiabatic and non-adiabatic dynamics methods under the BO framework. Specifically, we demonstrate that single BO molecular dynamics must include an extra nuclear Berry force in order to conserve total angular momentum, and non-adiabatic multi-surface dynamics methods like surface hopping are not well-defined when there are spin-related interactions and electronic degeneracies. To this end, we next propose a class of phase-space approaches based on a semiclassical phase-space electronic Hamiltonian, $\hat {H}{\rm PS} (\bm R, \bm P)$, that is parameterized by both nuclear position $\bm R$ and momentum $\bm P$. We demonstrate that propagating dynamics on phase-space potential energy surfaces, ${E}{\rm PS} (\bm R, \bm P)$, obtained by diagonalizing $\hat {H}_{\rm PS} (\bm R, \bm P)$ not only captures the nuclear Berry curvature effects in model systems but also correctly handles the electronic inertia effects in \textit{ab initio} simulations, allowing us to study angular momentum transfer processes. Finally, we find that phase-space approaches yield much better vibrational energies when non-adiabatic effects are strong. On the basis of this data, as combined with recent results showing that phase-space approaches can recover properties completely missing in the BO framework such as electronic momentum and vibrational circular dichroism -- this thesis submits that phase-space methods have great potential for advancing the study of theoretical chemistry beyond the BO framework.