In this chapter, several examples of NN fitting of databases obtained using either ab initio electronic structure methods or an empirical potential will be discussed. The objective of this presentation is not to provide a complete and comprehensive review of the field nor is it to acquaint the reader with the details of the reaction dynamics of the particular systems employed as examples. It is rather to provide a clear picture of the power and limitations of NN methods for the investigation of reaction dynamics. We begin with a brief overview of the literature in the field. Neural networks provide a powerful method to effect the fitting of an ensemble of potential energy points in a database. In 1993, Blank et al. employed an NN to fit data derived from an empirical potential model for CO chemisorbed on a Ni(111) surface. Two years later, these same investigators also examined the interaction potential of H2 on a Si(100)-2 × 1 surface using a data set comprising 750 energies computed using local density functional theory. To the best of our knowledge, these were the first two examples in which NNs were employed to provide the PES for a dynamics study. Hobday et al. have investigated the energies of C-H systems by using a Tersoff potential form in which the three-body term is replaced by an NN comprising five input nodes, one hidden layer with six nodes, and an output layer. In this work, the five input elements are computed by consideration of the bond type, i.e., C-C or C-H, the three-body bond angle θ, which is input to the NN in the form (1 + cos θ)2, the connectivity of the local environment, and the second neighbor information. The method was applied to carbon clusters and a wide variety of alkanes, alkenes, alkynes, aromatics, and radicals. Comparison of the atomization energies obtained using the NN potential surfaces with experimental values showed the errors for 12 alkanes, 13 alkenes, 4 alkynes, 7 aromatics, and 12 radicals to lie in the ranges zero to 0.3 eV (alkanes), 0.1 to 1.5 eV (alkenes), 0 to 0.5 eV (alkynes), zero to 1.0 eV (aromatics), and zero to 2.8 eV (radicals).