In this report some electrodynamics problems of materials with negative refraction are considered. It is shown that for such materials many laws and equations must be recorded in a different way than in usual case, when index of refraction is positive. In the most of books and textbooks so-called <i>nonmagnetic approach</i> is used, which is valid for nonmagnetic materials (μ=1) only. This approach cannot be applied with respect to materials with negative index of refraction. It is shown that materials with simultaneously negative dielectric and magnetic permeabilities undoubtedly must possess the frequency dispersion. Correlation between phase and group velocities is pointed out for such materials. A question of so-called <i>overcoming the diffraction limit</i> by means of plates from material with negative refractive index is considered in details. It is shown that this effect is indeed reduced to a problem of matching between a source and a receiver of radiation. Such matching is possible due to propagation of the evanescent modes, for which the diffraction limit does not exist. These modes fade on distances of order of a wavelength, and only on such a distance it is possible to transfer picture details which are smaller than wavelength.