The exact factorization of the time-dependent molecular wavefunction 1-4 has seen numerous applications in the domain of excited-state nonadiabatic dynamics based on the developments of novel "tools" of analysis and of trajectorybased algorithms for quantum molecular dynamics . The exact factorization implies a rewriting of the molecular timedependent Schrödinger equation as two coupled equations for the evolution of the electronic conditional amplitude and of the nuclear marginal amplitude. In particular, in formal analogy with the Born-Oppenheimer approximation -but clearly beyond this approximation, the nuclear evolution is expressed as a new effective time-dependent Schrödinger equation where the effect of the electrons in their ground state as well as in their excited states is encoded in a time-dependent vector potential and in a time-dependent potential energy surface that adapt in time to the nonadiabatic electronic dynamics. These potentials are the tools that have been applied in several occasions to provide an interpretation of dynamics in the presence of conical intersections alternative to the Born-Oppenheimer framework (and the Born-Huang expansion) . Following the study of these potentials, trajectorybased algorithms have been developed to approximate them within an on-the-fly molecular-dynamics scheme. In this way, electronic-structure information, in terms of energies, gradients and couplings, is used to reconstruct the time-dependent potentials along the nuclear trajectories .