We outline a new time-dependent wave packet formulation of quantum scattering theory. The theory obtains the differential cross section directly from the time-evolution of a plane wave packet, bypassing the usual S-matrix formulas. We introduce the theory for potential scattering, generalize it to reactive scattering, then explain how the theory was used recently to interpret the H+D-2-->HD (v=3 j=0)+D reaction in collaboration with experiment [S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. We also present new findings of quantum interference in the H+D-2 reaction.