It has recently become possible to solve quantum reactive scattering problems within their full three-dimensional context for three-atom systems with modest numbers of energetically-open initial-and-final quantum states. While a high level of accuracy has been achieved for a few simple systems, there remain major impediments to the extension of these methods to the vast majority of interesting chemical reactions. The basic theoretical and computational issues are easily characterized on a qualitative level. First, the complexity and computational intensity of current methods even for simple three-atom systems challenge current generations of high-performance computers. Second, as one moves beyond these simple chemical reactions, the complexity of the calculations increases tremendously because the number of open initial-and-final quantum states increases by orders of magnitude. For this reason such problems are currently beyond the realm of consideration for even the most optimistic of researchers. This research will focus on developments that will provide steps towards solving such problems on massively parallel computers.