Abstract: This paper provides an overview of theoretical solutions for shallow water equations and tropical wave characteristics. Additionally, systematic methods for identifying equatorial waves from observations are presented. Recent advancements in tropical wave observational studies have revealed several mechanisms that affect tropical wave evolution, such as wave–flow interaction, wave–cumulus convection interaction, and moisture mode. Local large-scale circulation and cumulus convection play a crucial role in controlling the structure, intensity, and movements of tropical waves. This paper also reviews the impact and mechanism of tropical waves on the formations and tracks of tropical cyclones. The multiscale variation of tropical cyclone activity can be explained by examining tropical waves. However, to advance tropical atmospheric dynamics, further research is necessary to address scientific problems related to atmospheric tropical waves.