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This dissertation reviews a number of works, which provide a thorough study of the quasi-normal spectrum of a wide class of black holes in four and higher dimensions for fields of various spin and gravitational perturbations. By the analysis of the quasi-normal spectrum, the stability of higher dimensional black holes has been studied. Special attention is paid to the evolution of massive fields in the background of various black holes. In addition, we present two new numerical techniques: a generalisation of the Nollert improvement of the Frobenius method for higher dimensional problems and a qualitatively new method, which allows to calculate quasi-normal frequencies for black holes, which metrics are not known analytically.
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