Review and comparison of MHD wave characteristics at the Sun and in Earth’s magnetosphere

Magnetohydrodynamic (MHD) waves play a crucial role in the plasma processes of stellar atmospheres and planetary magnetospheres. Wave phenomena in both media are known to have similarities and unique traits typical of each system. 
MHD waves and related phenomena in magnetospheric and solar physics are studied largely independently of each other, despite the similarity in properties of these media and the common physical foundations of wave generation and propagation. A unified approach to studying MHD waves in the Sun and Earth's magnetosphere opens up prospects for further progress in these two fields. 
The review examines the current state of research into MHD waves in the Sun’s atmosphere and Earth's magnetosphere. It outlines the main features of the wave propagation media: their structure, scales, and typical parameters. We describe the main theoretical models applied to wave behavior studies; discuss their advantages and limitations; compare characteristics of MHD waves in the Sun’s atmosphere and Earth’s magnetosphere; and review observation methods and tools to obtain information on waves in various media.