In the last years, Neural Networks (NNs) turned out as a suitable approach to map accurate Potential Energy Surfaces (PES) from ab initio/DFT energy data sets. PES are crucial to study reactive and nonreactive chemical systems by Monte Carlo (MC) or Molecular Dynamics (MD) simulations. Here we present a review of (a) the main achievements, from the literature, on the use of NNs to obtain PES and (b) our recent work, analyzing and discussing models to map PES, and adding a few details not reported in our previous publications. Two different models are considered. First, NNs trained to reproduce PES represented by the Lennard-Jones (LJ) potential function. Second, the mapping of multidimensional PES to simulate, by MD or MC, the adsorption and self-assembly of solvated organic molecules on noble-metal electrodes, focusing the ethanol/Au (111) interface. In both cases, it is shown that NNs can be trained to map PES with similar accuracy than analytical representations. The results are relevant in the second case, in which simulations by MC or MD require an extensive screening of the interaction sites at the interface, turning the development of analytical functions a nontrivial task as the complexity of the systems increases. a 997, 280, 171 are the number of energy points used in training. in reduced units). DC, diffusion coefficient. Within the parentheses are the errors of the properties using NN-generated PES relatively to the results using the analytical function. 1,312, 442, 267 are the number of energy points used in training. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 441 13. Malshe, M.; Raff, L. M.; Rockley, M. G.; Hagan, M.; Agrawal, P. M.; Komanduri, R.