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The field-theoretical approach is reviewed. Perturbations in generalrelativity as well as in an arbitrary $D$-dimensional metric theory are studiedon a background, which is a solution (arbitrary) of the theory. Lagrangian forperturbations is defined, and field equations for perturbations are derivedfrom the variational principle. These equations are exact and equivalent to theequations in the standard formulation, but can be approximate also. Thefield-theoretical description is invariant under gauge (inner) transformations,which can be presented both in exact and approximate forms. Following the usualfield-theoretical prescription, conserved quantities for perturbations areconstructed. Conserved currents are expressed through divergences ofsuperpotentials -- antisymmetric tensor densities. This form allows to relate anecessity to consider local properties of perturbations with a theoreticalrepresentation of the quasi-local nature of conserved quantities in metrictheories. Applications of the formalism in general relativity are discussed.Generalized formulae for an arbitrary metric $D$-dimensional theory are testedin the Einstein-Gauss-Bonnet gravity.

Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories