We study in detail a novel type of optical nanoantennas made of high-permittivity low-loss dielectric particles. In addition to the electric resonances, the dielectric particles exhibit very strong magnetic resonances at the nanoscale, that can be employed in the Yagi-Uda geometry for creating highly efficient optical nanoantennas. By comparing plasmonic and dielectric nanoantennas, we demonstrate that all-dielectric nanoantennas may exhibit better radiation efficiency also allowing more compact design.