Research on nanoantennas and metasurfaces based on high-index dielectric and semiconductor materials form a new branch in nanophotonics. Thanks to their strong interaction with both electric and magnetic components of light, resonant dielectric nanostructures provide a variety of opportunities, which were not possible in plasmonics. Silicon is now considered as one of the most promising materials for nanoantenna design. Having relatively small feature size (around 100-200 nm for resonances in the visible), resonant silicon nanostructure have a number of advantages compared to their plasmonic counterparts, including: very low losses in near-IR and visible spectrum; strong magnetic dipole response (much stronger than electric dipole in the certain wavelength range) and compatibility with CMOS nanofabrication. During this seminar, I will review several recent results of our team, which demonstrate a huge potential of resonant dielectric nanostructures for a variety of applications. This will include: (i) magnetic near-field enhancement in silicon nanoantennas, (ii) low-loss light guiding in resonant Si nanoparticle chains, (iii) highly-efficient visible light bending with dielectric metasurfaces, and (iv) generalized Brewster effect in dielectric metasurfaces with strong magnetic response.