**Abstract**

The boson peak in the terahertz range is the low-energy excitations in glasses and disordered crystals. It is related to the excess part of the vibrational density of states. Borate glass is one of the typical network oxide glasses with covalent bonds and belongs to the strong type of glass formers. Alkali metal ions are well-known modifiers of the borate glass network and control various properties. The alkali metal effects are reviewed on basic physical properties such as elastic constants, density, and vibration modes in relation to the variation of structural units in a modified borate glass network. The alkali effect on a boson peak is discussed on the basis of experimental results of neutron inelastic scattering, neutron diffraction, Raman scattering, and heat capacity at low temperatures. The correlation is discussed between the boson peak frequency, the peak temperature of excess heat capacity, and shear modulus. The static and dynamical correlation lengths are also discussed.

**Keywords:** borate glass, boson peak, FSDP, medium range order, fragility, relaxation, excess heat capacity
