This review covers the recent progress of studies on dynamics in the glassy states and near the glass transition of amorphous polymers as revealed by inelastic and quasielastic neutron scattering, covering four topics: (i) low energy excitation (boson peak) in the glassy states; (ii) fast process in picosecond order; (iii) E-process related to conformational transitions; (iv) dynamical heterogeneity as revealed by non-Gaussian parameter.Keywords. Amorphous polymers, Inelastic and quasielastic neutron scattering, Boson peak, Dynamics near T g , Fast process, E-process, Heterogeneity