  The field-theoretical approach is reviewed. Perturbations in general
relativity as well as in an arbitrary $D$-dimensional metric theory are studied
on a background, which is a solution (arbitrary) of the theory. Lagrangian for
perturbations is defined, and field equations for perturbations are derived
from the variational principle. These equations are exact and equivalent to the
equations in the standard formulation, but can be approximate also. The
field-theoretical description is invariant under gauge (inner) transformations,
which can be presented both in exact and approximate forms. Following the usual
field-theoretical prescription, conserved quantities for perturbations are
constructed. Conserved currents are expressed through divergences of
superpotentials -- antisymmetric tensor densities. This form allows to relate a
necessity to consider local properties of perturbations with a theoretical
representation of the quasi-local nature of conserved quantities in metric
theories. Applications of the formalism in general relativity are discussed.
Generalized formulae for an arbitrary metric $D$-dimensional theory are tested
in the Einstein-Gauss-Bonnet gravity.
