We review some recent developments in glassy dynamics research using neutron scattering. We focus on the following three topics: (i) low-energy excitation, (ii) fast process, (iii) dynamic heterogeneity in glassy state. In the fast and second topics, we show that recent research on glassy materials with various degrees of disorder provide useful information about the microscopic origin of low-energy excitation and fast β process. In the third topic, a non-Gaussian parameter is introduced to evaluate dynamic heterogeneity of glassy materials through mean square displacement, and a correlation between the non-Gaussian parameter and fragility index is pointed out. Distribution functions of the mean square displacement are evaluated on the basis of Gaussian, log-Gaussian and bimodal distributions.