  Atomic nuclei are composite systems, and they may be dynamically excited
during nuclear reactions. Such excitations are not only relevant to inelastic
scattering but they also affect other reaction processes such as elastic
scattering and fusion. The coupled-channels approach is a framework which can
describe these reaction processes in a unified manner. It expands the total
wave function of the system in terms of the ground and excited states of the
colliding nuclei, and solves the coupled Shr\"odinger equations to obtain the
$S$-matrix, from which several cross sections can be constructed. This approach
has been a standard tool to analyze experimental data for nuclear reactions. In
this paper, we review the present status and the recent developments of the
coupled-channels approach. This includes the microscopic coupled-channels
method and its application to cluster physics, the continuum discretized
coupled-channels (CDCC) method for breakup reactions, the semi-microscopic
approach to heavy-ion subbarrier fusion reactions, the channel coupling effects
on nuclear astrophysics and syntheses of superheavy elements, and inclusive
breakup and incomplete fusion reactions of weakly-bound nuclei.
