The talk is focused on studying diffraction of light (optical beams, pulses, and plane waves) by resonant optical structures. The particular structures considered are diffraction gratings (photonics crystal slabs) and phase-shifted Bragg gratings. Resonant optical and magneto-optical properties of these structures are investigated by studying structures’ eigenmodes. In the first part of the talk, a brief introduction to the concepts of the grating's scattering matrix, quasiguided modes, and Fano resonances will be given. New methods for calculating eigenmodes of resonant structures will be presented. Spatiotemporal formulation of the coupled-mode theory will be used to obtain a generalization of the Fano line shape of the resonance. This generalization gives simple approximations of the grating’s spatiotemporal transmission spectrum (taking into account both frequency and direction of the incident light). In the second part of the talk, these approximations will be used to derive a general form of optical signal spatiotemporal transformation implemented by resonant optical structures. The particular transformations investigated are the temporal and spatial differentiation of an optical signal. The last part of the talk covers the study of magneto-optical effects in resonant optical structures. In particular, resonances of Faraday and Kerr effects are studied by analyzing structure’s symmetry properties.