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A survey of recent results of the author in resonant light scattering by individual nanoparticles is presented. It is shown that in many cases of practical interest the scattering has very little in common with the conventional Rayleigh one. The main attention is paid to the so-called anomalous scattering and absorption, Fano resonances, tailoring of the scattering diagrams, etc. Another discussed subfield is a non-steady scattering of short pulses. It is shown that at high-Q resonances the non-steadiness of the scattering may give rise to qualitatively new effects, which do not exist in the steady-state scattering.