Investigations of the steady-state and transient electrical capacitance properties of semiconductor heterostructures allow determination of the conduction-band and valence-band energy offsets that occur at the interfaces between materials of different band-gaps and of the presence of carrier-trapping states both in the materials and at the interfaces. For determination of band offsets, the main technique is C-V measurement, i.e. the measurement of the steady-state small-signal (differential) capacitance as a function of applied voltage, and this paper outlines the C-V Intercept and C-V Charge-Profile Methods. Concerning electron and hole trapping in heterostructures, including that in quantum well structures, the presence, concentrations and energy levels of such carrier trapping states can be effectively determined by the C-V-T and DLTS techniques. This paper outlines the principles of these techniques for studying heterostructures, and gives examples of data and results. (C) 1999 Elsevier Science Ltd. All rights reserved.