Abstract: Understanding of the universal low-temperature properties of glasses and why they differ from their crystalline counterparts requires the understanding of the vibrational properties of glasses. Due to recent advances of computational techniques, we are now able to study simulated glasses with a wide range of vibrational properties, which is essential to understanding their role in the low-temperature properties of glasses. In this talk I will discuss the stability dependence of the vibrational modes of glasses ranging from poorly annealed to exceptionally stable. Our most stable glasses are comparable to exceptionally-stable, vapor- deposited laboratory glasses. We find that the density of quasi-localized, low-frequency modes decrease quickly with increasing stability and the density of these modes are correlated with sound attenuation in the harmonic approximation. We use a recently developed theory that very accurately reproduces the low-frequency sound attenuation to examine the relationship between the vibrational modes and sound attenuation. This theory indicates that the non- affine forces, which are responsible for the renormalization of the speed of sound in amorphous solids, is responsible for sound attenuation. Surprisingly, we find that the low- frequency, quasi-localized modes make a relatively small contribution to the sound attenuation coefficient compared to the extended, low-frequency modes. I will conclude by discussing recent attempts at identifying regions of the glass that play an enhanced role in sound attenuation, if they exist.