<p><em>[eng] Rossby waves are a pervasive feature of the large-scale motions of the Earth’s</em></p><p><em>atmosphere and oceans. These waves (also known as planetary waves and r-modes) also</em></p><p><em>play an important role in the large-scale dynamics of different astrophysical objects such as</em></p><p><em>the solar atmosphere and interior, astrophysical discs, rapidly rotating stars, planetary and</em></p><p><em>exoplanetary atmospheres. This paper provides a review of theoretical and observational</em></p><p><em>aspects of Rossby waves on different spatial and temporal scales in various astrophysical</em></p><p><em>settings. The physical role played by Rossby-type waves and associated instabilities is discussed </em></p><p><em>in the context of solar and stellar magnetic activity, angular momentum transport in</em></p><p><em>astrophysical discs, planet formation, and other astrophysical processes. Possible directions</em></p><p><em>of future research in theoretical and observational aspects of astrophysical Rossby waves are</em></p><p><em>outlined.</em></p>