  The boson peak (BP) is an excess of vibrational states over the Debye law
appearing at terahertz frequencies. It is found in all glasses and marks the
crossover between the long-wavelength behavior, where the solid can be
considered as an isotropic continuum, and the region where the wavelength of
the sound wave starts to experience the microscopic details of the structure.
This chapter is devoted to a review of the main experimental observations
regarding the vibrational dynamics of amorphous solids, as detected by neutron
and X-ray scattering techniques. A first part of the chapter is devoted to the
measurements of the BP and its evolution as a function of external parameters,
such as temperature, pressure, or density. The second part of the chapter
reviews the wavevector evolution of the dynamic structure factor, which
provides evidence of a pseudo-acoustic propagating mode up to frequencies
comparable to those of the BP. This longitudinal mode has a sound attenuation
which follows the Rayleigh scattering law and a negative dispersion that can
partially explain the deviation from the Debye law. At higher frequencies, the
inelastic spectrum presents a complex pattern of vibrations, with evidences of
two peaks in various systems. To conclude, we will highlight the information
that can be gained on the nature of the glass vibrational modes from a
comparison with the dynamics of the corresponding polycrystal.
