  A hallmark of glasses is an excess of low-frequency, nonphononic vibrations,
in addition to phonons. It is associated with the intrinsically nonequilibrium
and disordered nature of glasses, and is generically manifested as a THz peak
-- the boson peak -- in the ratio of the vibrational density of state (VDoS)
and Debye's VDoS of phonons. Yet, the excess vibrations and the boson peak are
not fully understood. Here, using reanalysis of experimental data, extensive
computer simulations and a mean-field model, we show that the nonphononic part
of the VDoS itself features both a universal power-law tail and a peak,
entirely accounted for by quasi-localized nonphononic vibrations, whose
existence was recently established. We explain the mild variation of the peak's
frequency and magnitude with glasses' thermal history, along with the strong
variation of the power-law tail. We also show that modes that populate the
peak's region feature many coupled quasi-localized nonphononic vibrations, when
their spatial structure is considered. Our results provide a unified physical
picture of the low-frequency vibrational spectra of glasses, and in particular
elucidate the origin, nature and properties of the boson peak.
