The article is dedicated to the anniversary of the discovery of Alfvén waves. The concept of Alfvén waves has played an outstanding role in the formation and development of cosmic electrodynamics. A distinctive feature of Alfvén waves is that at each point in space the group velocity vector and the external magnetic field vector are collinear to each other. As a result, Alfvén waves can carry momentum, energy, and information over long distances. We briefly describe two Alfvén resonators, one of which is formed in the ionosphere, and the second presumably exists in Earth’s radiation belt. The existence of the ionospheric resonator is justified theoretically and confirmed by numerous observations. The second resonator is located between reflection points located high above Earth symmetrically with respect to the plane of the geomagnetic equator.