Simulating the dynamics of a molecule initiated in an excited electronic state constitutes a rather challenging task for theoretical and computational chemistry, as such dynamics leads to a strong coupling between nuclear motion and electronic states, that is, a breakdown of the Born-Oppenheimer approximation. This New Views article proposes a brief overview on recent theoretical developments aiming at simulating the excited-state dynamics of molecules-nonadiabatic molecular dynamics-focusing in particular on strategies employing travelling basis functions to portray the dynamics of nuclear wavefunctions. We start by discussing the central equations for nonadiabatic molecular dynamics in a Born-Huang representation. We then propose a comparison between two commonly employed strategies to simulate the excited-state dynamics of molecular systems in their full configuration space, Ab Initio Multiple Spawning (AIMS) and Trajectory Surface Hopping (TSH). The equations of motion for the two techniques are compared and used to contrast their respective description of phenomena involving the decoherence of nuclear wavepackets. Some recent works and developments of the AIMS method are then summarised. This New Views article ends with a highlight on the Exact Factorisation of the molecular wavefunction and how this approach contrasts with the more conventional Born-Huang picture when it comes to the description of photophysical and photochemical processes.