Recent developments in high-pressure in situ Brillouin spectroscopy of a simple molecular system are reviewed by demonstrating experimental and analytical methods for the study of acoustic velocities in any direction, adiabatic elastic constants, and elastic anisotropy. Detailed applications to solid argon (Ar) are presented, at pressures up to 70 GPa in a diamond anvil cell, using recently developed approaches that combine the method of in situ Brillouin spectroscopy, for a single crystal of Ar up to 4 GPa, and the envelope method applied to both longitudinal acoustic and transverse acoustic modes, for recrystallized Ar between 4 and 70 GPa.