Recent results in magnonics – a topical and rapidly developing branch of spintronics and magnetoelectronics – are presented. The paper describes measurement techniques and theoretical approaches used to explore physical processes associated with the spin-wave propagation in complex nano- and micro-dimensional magnetic structures. The results of the application of magnetic structures in signal processing and transmission systems are discussed. In particular, results on spin wave propagation in distributed magnetic periodic structures, lumped systems, coupled waveguide structures, and controllable magnonic structures are considered. Specific examples of circuitry based on magnonic structures are discussed, and possibilities for further developing this circuitry are explored.