Specific properties of all-dielectric metamaterials and engineered dielectric structures will be discussed in the context of their application for providing negative refraction, energy confinement, antenna miniaturization, and cloaking. Special attention will be paid to coupling, resonance splitting, and metamaterial homogenization problems in cloaking devices. Several dielectric-based cloaking approaches will be outlined. Finally, formation of Fano resonances in all-dielectric metamaterials will be demonstrated and discussed.