The introduction of the time-dependent potentials in the framework of the exact factorization, along with a natural analogy with classical electromagnetism, lends itself to the introduction of the concept of a classical force , that is uniquely defined in the framework of the exact factorization. The concept of a classical force goes hands in hands with that of trajectories 109 : in this way, the formalism has been employed successfully and largely in the domain of quantum molecular dynamics and of on-the-fly simulations . Perhaps, this is the field where the exact factorization made the most progress and proposed the most interesting developments, some of which will be discussed in this Perspective.