The mechanisms of current through insulators in the presence of surface potential barriers and electron traps are discussed, and the simplified theory of space-charge-limited current through insulating solids is described. The steady-state equations for one-dimensional single-carrier current are derived and approximate solutions are given; theoretical current/voltage characteristics are calculated and indicate that large currents could flow and that their characteristics could be utilized in practical devices. The continuity equations for time-varying current are derived for the case when electron transit times and trapping relaxation times are both significant.Experiments are described which have demonstrated some of the predicted characteristics of space-charge-limited current; in particular a threshold voltage for current, a square-law dependence of current upon applied voltage, and rectification have been observed. The currents are of practical magnitudes; steady and reproducible current densities of several amperes per square centimetre have been drawn through insulating crystals of cadmium sulphide at room temperature with a few volts applied. Measurements with microsecond pulses have shown that there is no detectable delay by the crystal in responding to a pulse rise or fall time of the order of 0.1 microsec; there seems no fundamental reason why response times as short as 0.1 milli-microsec should not be expected.It is apparent that many new types of solid-state device may be developed by exploiting current in insulators. Some possible applications are discussed, including a dielectric triode which should combine the high input impedance of the vacuum triode with the high current output of the transistor and have a gain-bandwidth product as great as that of either device. The technical difficulties involved in developing space-charge-limited dielectric devices seem no greater than those successfully overcome in developing presently available semiconductor devices.