Understanding the state-resolved dynamics of elementary chemical reactions involving polyatomic molecules, such as the well-known reaction mechanism of nucleophilic bimolecular substitution (SN2), is one of the principal goals in chemistry. In this Review, the progress in the quantum mechanical treatment of SN2 reactions in the gas phase is reviewed. The potential energy profile of this class of reactions is characterized by two relatively deep wells, which correspond to pre- and post-reaction chargedipole complexes. As a consequence, the complex-forming reaction is dominated by Feshbach resonances. Calculations in the energetic continuum constitute a major challenge because the high density of resonance states imposes considerable requirements on the convergence and the energetic resolution of the scattering data. However, the effort is rewarding because new insights into the details of multimode quantum dynamics of elementary chemical reactions can be obtained.