When neutrons are scattered by interacting with atomic nuclei in a material, both their direction and energy generally change. Up to the previous chapter, we have dealt with scattering where the energy does not change, namely, elastic scattering. In this chapter, however, we will discuss scattering where the energy changes slightly, that is, quasielastic neutron scattering. We will start with the differences between quasielastic and elastic scattering, and then describe the information that can be obtained from quasielastic neutron scattering using the dynamic structure factor and the space-time correlation function. Furthermore, we will also provide an overview of the high-energy-resolution Neutron Spin Echo spectroscopy.