The properties of narrow superconducting channels carrying a direct current are reviewed. Among the topics covered are the stability of the normal state of the current-carrying channel and the mechanism for a transition from this normal state to the superconducting state. In a homogeneous channel, the transition occurs through the formation of a critical nucleus and is a first-order phase transition. In a channel with inhomogeneities, the transition is quite different. In this case the normal state can exist only down to a certain value of the current, below which the normal state is absolutely unstable. The review is devoted primarily to the theory of the resistive state of narrow channels, which exists at currents above the critical Ginzburg--Landau current. The description is based on the concept of phase-slippage centers. Phenomenological models are discussed, as is a model of a fluctuational excitation of phase-slippage centers. The results obtained from the microscopic dynamic theory of superconductivity are discussed at length. Among these results are the voltage-current characteristic of the resistive state, the abrupt change in the voltage on this characteristic, and the structure of the phase-slippage centers.