Topological states offer advantages such as resistance to interference, suppression of scattering, and high error tolerance, which provides a robust platform for realizing photonic functional devices. A topological rainbow is a frequency-splitting device based on topological states. By precisely designing the geometric structure of a topological insulator, it can separate topological states of different frequencies and trap them in distinct spatial locations, achieving demultiplexing effects. This concept holds great potential for applications in the design and implementation of devices such as topological routing, topological slow light, high-capacity information storage, and broadband information processing. We review recent research progress on topological rainbows, focusing primarily on theoretical and experimental studies in optical systems, while also covering typical classical wave systems such as acoustics and elastic waves. We first introduce the physical principles of topological rainbows, then summarize and analyze the realization schemes of topological rainbows, categorizing them into three types: topological rainbows based on dispersion engineering, topological rainbows based on synthetic dimensions, and topological rainbows based on Landau levels. Finally, the challenges faced in the physical realization and functional applications of topological rainbows are discussed, along with future development directions.