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Background: Resonant light scattering by nanoparticles provides the unique opportunity to concentrate a high-amplitude electromagnetic field and to tailor and control its pattern in a subwavelength area of space. In addition to purely academic interest, this is extremely important for numerous applications ranging from medicine and biology to telecommunication and data processing. Objective: To examine new effects in this subfield, especially those associated with the Mie and Fano resonances. Methods: The primary attention is paid to the theory of the phenomenon. The description employs exactly solvable problems, tractable models, and numerical methods. Results: It is shown that in many cases, despite the smallness of the scattering particles, their light scattering has very little in common with the conventional Rayleigh case. New, counterintuitive effects, especially those related to the violation of the quasi-static description of the scattering occurring at the action of (ultra)short laser pulses, are pointed out and inspected. These new types of scattering are discussed and classified. Conclusion: Despite more than a hundred years of extensive study of light scattering by small particles, the problem is still far from completion. Its new subfields correspond to resonant modes' selective excitation, interferences, and dynamic effects at "swinging" of high-Q resonances. Acknowledgment: The author acknowledges the financial support of the Russian Foundation for Basic Research (Projects No. 20-02-00086) for the analytical study and modeling of the resonant light scattering, as well as the contribution of the Russian Science Foundation for the computer simulation (Project No. 21-12-00151), and the provision of user facilities (Project No. 19-72-30012).