In XF, the electronic-nuclear wave function is factorized into the product of nuclear and electronic wave functions, which follow their own equations of motion (EOMs) and are coupled with each other through the time-dependent potential energy surface (TDPES), the time-dependent vector potential (TDVP) and the electron-nuclear coupling operator (ENCO). XF provides a new route to introduce approximations and develop better nonadiabatic dynamics methods. With a series of approximations, the coupled-trajectory mixed quantum-classical (CTMQC) method has been derived, which results in an Ehrenfest-like dynamics with an extra "quantum momentum" term in both the nuclear and electronic EOMs. This term can describe the branching of nuclear WP and the collapse of electronic wave function (i.e., decoherence), which are absent in the traditional EMF dynamics. Considering the close relation between EMF and SH, coupled-trajectory surface hopping (CTSH) was also proposed by using an adiabatic force instead of the full CTMQC force to drive the nuclear motion. This leads to better numerical stability at long time and nuclear WP branching can also be naturally depicted by SH trajectories. As a coupled-trajectory framework, the electronic wave functions of the trajectories are coupled with each other through the quantum momentum in both CTMQC and CTSH, whose computational cost scales quadratically with the number of trajectories. To increase the efficiency, the SH based on exact factorization (SHXF) metod has been proposed. Independent trajectories are used instead of a coupled-trajectory ensemble, and the quantum momentum is derived from auxiliary trajectories. Both CTSH and SHXF rely on trajectories moving on the active PESs, which are allowed to hop between PESs in a stochastic way.