Capacitance transient spectroscopy, frequency resolved capacitance spectroscopy and the Hall effect have been used as a function of temperature to characterise deep levels in some III-V semiconductor materials. Hydrostatic pressure has been used to move the energy bands and study the pressure dependence of the activation energy of deep levels. These experimental methods have been developed with the aim of measuring the pressure coefficients of impurity levels due to transition metals in order to establish whether their position relative to the vacuum level is fixed and Independent of the host material as has been suggested by Ledebo and Ridley (1982). The pairing of the transition metal acceptor Mn with a donor from group VI has been studied in the quaternary alloy GalnAsP and shown to lend negligible carrier scattering in certain circumstances. Electron emission from quantum wells has been investigated as a function of temperature and pressure to measure conduction band-offsets and their pressure dependence.