The time-dependent quantum wave packet approach has been improved and formulated to treat the multiple surface problems and thus provided a new simple, yet a clear quantum picture for interpreting the reaction mechanism underlying the nonadiabatic dynamical processes. The method keeps the salient feature of the original quantum wave packet theory developed for single surface problems, i.e. the introduction of the absorbing potential and the grid basis including the discrete variable representation and the fast Fourier transformation, which makes the present methodology a very efficient implement for the nonadiabatic quantum scattering calculations. Here, we review the theoretical basis of this approach and its applications to the fundamental triatomic chemical reactions, the latter include the nonadiabatic dynamics calculations on the F + H₂, F + HD, F + D₂, O(¹D) + N₂, O(³P, ¹D) + H₂, D⁺ + H₂, and H⁺ + D₂ reactions. We also present a thorough historical overview of the theoretically nonadiabatic dynamical investigations particularly on the triatomic systems, and show how the time-dependent wave packet approach complements the time-independent quantum scattering theory.