In general, the exact-factorization-based algorithms derived so far can be viewed as variations of the Ehrenfest scheme or of the surface-hopping method, where the effect of the quantum momentum is included. The advantage of these particular formulations is twofold: first, since Ehrenfest and surface hopping are the most widely-used approaches for simulations of photochemical processes, they are well-understood by the community and are implemented in many codes; second, it is easy to show how the corrections related to the inclusion of the quantum momentum cure the major drawbacks of both approaches, i.e., the mean-field character of Ehrenfest 171 and the overcoherence problem of surface hopping FIG. . Left panels: Ehrenfest dynamics (using 1000 trajectories). Right panels: Surface hopping dynamics (using 2000 trajectories). In the upper panels, the ground-state (dark-green line) and the excitedstate (orange line) potential energy curves are shown, along with the quantum nuclear density at three times along the simulated dynamics compared to the Ehrenfest or surface hopping trajectories at the same times. In the lower panels, the population of the excited state is shown as black curves, superimposed to the population estimated during Ehrenfest dynamics (left) or during surface hopping dynamics (right).