Inelastic scattering of light caused by acoustic phonons was first predicted by Léon Brillouin in 1914
. Leonid Mandelstam is believed to have recognised the possibility of such scattering as early as 1918, but he published his idea only in 1926.
In order to credit Mandelstam,  the effect is also called Brillouin-Mandelstam scattering (BMS). Other commonly used names are Brillouin light scattering (BLS) and Brillouin-Mandelstam light scattering (BMLS).
The process of stimulated Brillouin scattering (SBS) was first observed by Chiao et al. in 1964. The optical phase conjugation aspect of the SBS process was discovered by Boris Yakovlevich Zeldovich et al. in 1972.