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.