The theoretical methodology for including the effects of the geometric phase in quantum reactive scattering and bound-state calculations is reviewed. Two approaches are discussed: one approach is based on solving the standard Born-Oppenheimer equation but with double-valued boundary conditions, and the second approach is based on solving a generalized Born-Oppenheimer equation with single-valued boundary conditions. The generalized Born-Oppenheimer equation contains a vector potential which is mathematically equivalent to that of a magnetic solenoid. The recently developed numerical methodology for solving the generalized Born-Oppenheimer equation is reviewed, and several applications of this methodology in chemical reaction dynamics and molecular spectra are discussed. New results from accurate six dimensional quantum reactive scattering calculations for the D + H-2(v, j) --> HD(v', j') + H and H + H-2(V,j) --> H-2(v('), j') + H reactions are presented. These calculations are performed both with and without the geometric phase. The geometric phase calculations are done using both the double-valued basis set approach and vector potential approach. The effects of the Geometric phase in the reaction probabilities, integral, and differential cross sections are investigated as a function of scattering energy and total angular momentum J.