State-of-the-art studies of dielectric magnonics and magnon spintronics are reviewed. Theoretical and experimental approaches to exploring physical processes in and calculations of the parameters of magnonic micro-and nanostructures are described. We discuss the basic concepts of magnon spintronics, the underlying physical phenomena, and the prospects for applying magnon spintronics for data processing, transmission, and reception. Special attention is paid to the feasibility of boosting the operating frequencies of magnonic devices from the gigahertz to terahertz frequency range. We also discuss specific implementations of the component base of magnonics and ways to further develop it.