Resonant nanostructures made of high-refractive index dielectric materials offer a new way for manipulation of light at nanoscale. Due to their inherently high magnetic and electric resonant response and low losses at optical frequencies these nanostructures offers unique functionalities, which are not achievable with conventional nanoscale plasmonics. Simple examples are strong magnetic near-field enhancement and directional scattering by nanoparticles of spherical shape, also known as a Kerker’s effect. At this seminar, I will review this new rapidly developing research direction and present several new results of our team, which demonstrate a huge potential of dielectric nanoantennas for various applications. Fist will be experimental demonstration of highly localized magnetic and electric fields in silicon nanodimer antennas, which can be excited at any polarization of incoming light. Second will show low-loss light propagation in silicon nanoparticle waveguides, which can be much longer than in plasmonic waveguide of similar dimensions. Third will present how the light can be manipulated with almost fully transparent resonant dielectric metasurfaces having a full 2? control over the phase of incoming light at visible and near-IR wavelengths. And finally I will introduce new type of generalized Brewster effect, which can be achieved at dielectric metasurfaces with strong magnetic response.