The study of solids at high pressure and variable temperature enables development of accurate interatomic potential functions over wide ranges of interatomic distances. A review of the main models used in the determination of these potentials is given in Chapter one. A discussion of phonon frequency as a variable physical parameter reflecting the interatomic potential is given. A high pressure Raman study of inorganic salts of the types MSCN, (M = K,Rb,Cs & NH4+) and MNO2, (M = K,Na) has been completed. The studies have revealed two new phases in KNO2 and one new phase in NaNO2 at high pressure. The accurate phonon shift data have enabled the determination of the pure and biphasic stability regions of the phases of KNO2. A discussion of the B1, B2 relationship of univalent nitrites is also given. In the series of thiocyanates studied new phases have been found in all four materials. In both the potassium and rubidium salts two new phases have been detected, and in the ceasium salt one new phase has been detected, all at high pressure, from accurate phonon shift data. These transitions are discussed in terms of second-order mechanisms with space groups suggested for all phases, based on Landau's theory of second-order phase transitions. In the ammonium salt one new phase has been detected. This new phase transition has been interpreted as a second-order transition. The series of molecular crystals CH3HgX, (X = Cl,Br & I) has been studied at high pressure and at variable temperature. In Chapter five, their phase behaviour at high pressure is detailed along with the pressure dependencies of their phonon frequencies. In the chloride and the bromide two new phases have been detected. In the bromide one has been detected at high temperature and one at high pressure, the latter being interpreted as the stopping of the methyl rotation. In the chloride one phase has been found at both low temperature as well as high pressure, and the other only at high pressure, the latter again associated with the stopping of methyl rotation. The iodide displays two high pressure transitions. A Raman-active soft-mode has been observed in all three analogues, at both high pressure and variable temperature. For the chloride and bromide analogues there is a discussion of the nature of the soft-mode along with the mechanism associated with the I/II transition. The results of the X-ray crystal structure determination of CH3HgBr at ambient temperature and pressure are given.