A review dedicated to the contemporary methods of quantization of the gravitational field. In view of possible applications to elementary particle theory, the authors consider only asymptotically flat gravitational fields. The basis of the exposed method of quantization is the method of quantization of gauge fields in the functional integration formalism. The main result is the formulation of covariant rules for a diagrammatic perturbation theory. Its elements are the lines representing gravitons and the vertices of graviton-graviton interaction, as well as the lines and interaction vertices of fictitious vector particles (``Faddeev--Popov ghosts'') characteristic for the theory of gauge fields. The expressions for the propagators and vertex functions are given explicitly. It is shown that the presence of fictitious particles in the covariant diagram technique guarantees the unitarity of the theory and the agreement between the covariant quantization with the canonical quantization. The bibliography contains 44 entries (54 names).