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The basic principles of one- and two-carrier, volume-controlled injection currents are reviewed. One-carrier injected currents are necessarily space-charge-limited and are strongly affected by the presence of traps which usually capture and immobilize most of the injected carriers. The trapped carriers are in an effective thermal equilibrium with the free injected carriers. The concepts of "shallow" and "deep" traps are defined and their effects on injected currents studied. It is shown that the presence of "deep" traps leads to a very steep rise of current with voltage, resembling a breakdown curve, at an appropriate voltage. Under double injection, that is, the simultaneous injection into the insulator of electrons from a cathode and holes from an anode, space-charge limitations are at least partially overcome but recombination of injected carriers presents a new limitation on the current flow. In any insulator at sufficiently high injection levels both recombination and space charge contribute to limitation of the current, leading to a dependence of current on the cube of the voltage, for monomolecular recombination processes. For double injection into a semiconductor, the presence of thermally generated free carriers leads to charge neutrality (the so-called ohmic relaxation process) and recombination alone limits the current. In a semiconductor long compared to a diffusion length this leads to a dependence of current on the square of the voltage.