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A comprehensive review of the problem of applications of a laser action on nanoparticles in biology and medicine is presented. The main attention is paid to the new results in light scattering by subwavelength particles (such as the anomalous scattering, Fano resonances, design and tailoring of scattering diagrams, etc.). Heating of a nanoparticle by a laser pulse is also discussed in detail. The problem of the optimization of the heating, affected by the energy transfer to the surrounding particle biological tissue, is posed and inspected. It is shown that the proper choice of the problem parameters may considerably enhance the therapeutic effects of the laser treatment, while undesirable side effects may be considerably reduced.