The Born‐Oppenheimer approximation constitutes a cornerstone of our understanding of molecules and their reactivity, partly because it introduces a somewhat simplified representation of the molecular wavefunction. However, when a molecule absorbs light containing enough energy to trigger an electronic transition, the simplistic nature of the molecular wavefunction offered by the Born‐Oppenheimer approximation breaks down as a result of the now non‐negligible coupling between nuclear and electronic motion, often coined nonadiabatic couplings. Hence, the description of nonadiabatic processes implies a change in our representation of the molecular wavefunction, leading eventually to the design of new theoretical tools to describe the fate of an electronically‐excited molecule. This Overview focuses on this quantity—the total molecular wavefunction—and the different approaches proposed to describe theoretically this complicated object in non‐Born‐Oppenheimer conditions, namely the Born‐Huang and Exact‐Factorization representations. The way each representation depicts the appearance of nonadiabatic effects is then revealed by using a model of a coupled proton–electron transfer reaction. Applying approximations to the formally exact equations of motion obtained within each representation leads to the derivation, or proposition, of different strategies to simulate the nonadiabatic dynamics of molecules. Approaches like quantum dynamics with fixed and time‐dependent grids, traveling basis functions, or mixed quantum/classical like surface hopping, Ehrenfest dynamics, or coupled‐trajectory schemes are described in this Overview
