Various algorithms based on the exact factorization are capable to circumvent naturally at the same time the mean-field and overcoherence issues of Ehrenfest and surface hopping thanks to the presence of the quantum momentum. In the past few years, different groups introduced different flavours of quantum-classical algorithms: the coupled-trajectory mixed quantum-classical (CTMQC) scheme was developed by Gross and coworkers in 2015 , and as the name says, it employs an ensemble of coupled trajectories to mimic the nuclear dynamics; later on, the method surface hopping based on the exact factorization (SHXF) was introduced by Min and coworkers in 2018 , aiming to use a surface-hopping scheme to mitigate the problems related to the large computational cost of CTMQC by evolving independent trajectories and adopting auxiliary trajectories when necessary; with a similar purpose, in 2021, Pieroni and Agostini developed the coupledtrajectory Tully surface hopping (CTTSH) , which uses the idea of surface hopping within a coupled-trajectory procedure; Ha and Min proposed in 2022 an independent-trajectory version of CTMQC, named Ehrenfest dynamics based on the exact factorization (EhXF) , which requires auxiliary trajectories similarly to SHXF; aiming to alleviate the issue of non-conservation of the total energy in CTMQC, Villaseco Arribas and Maitra introduced in 2023 a variation of the algorithm, i.e., CTMQC-E , by imposing energy conservation over the ensemble of trajectories, following a similar idea that in EhXF is imposed at the single-trajectory level; in a similar spirit, Blumberger and coworkers developed in 2023 CTMQC-(E)DI , where a double-intercept (DI) idea is introduced in CTMQC and in CTMQC-E to cure numerical instabilities encountered in CTMQC(-E) when calculating the quantum momentum and, thus, greatly improving energy and norm conservation; in 2024 Maitra and coworkers, inspired by the work , developed the quantumtrajectory surface-hopping based on the exact factorization (QTSH-XF) , where a phase-space approach combined with the exact factorization cures the frustrated hops and velocity rescaling issues that SHXF inherits from surface hopping; an assessment of various exact-factorization-based algorithms, i.e., those based on auxiliary trajectories, along with their implementation in the Libra package 195 has been recently presented by . Currently, to the best of our knowledge, the available open-source codes able to perform exact-factorization-based calculations are PyUNIxMD 190 , developed in the group of Min and interfaced with various quantum-chemistry packages, G-CTMQC 196 , developed by our group and interfaced with the QuantumModelLib library of analytical potentials 197 , and Libra 191 , which for the moment only allows calculations with model potentials; CTTSH has been recently implemented in MOPAC-PI .