Rainbow trapping is a wave localization phenomenon in which different frequencies are spatially separated and confined by engineering dispersion through structural gradients. Initially demonstrated in tapered metamaterial systems, this concept has since been extended to plasmonic, photonic, acoustic, and elastic platforms, where graded-index profiles, chirped periodicities, and tapered geometries are used to control the group velocity and localize wave components at distinct spatial positions. These implementations enable highresolution spectral manipulation and form the foundation for broadband wave control. More recently, topological rainbow trapping has emerged as a robust alternative, leveraging topologically protected states to achieve disorder-immune frequency localization. This approach offers enhanced resilience to fabrication imperfections and opens new possibilities for scalable, integrated wave-based devices. In this review, we examine the physical mechanisms, system-specific implementations, and recent advances in both conventional and topological rainbow trapping. We also highlight promising applications ranging from optical communication and wavelength multiplexing to acoustic wave manipulation and vibrational energy harvesting and discuss key challenges and future directions in this rapidly evolving field.