Distributed Brillouin fiber sensing realizes continuous measurement of temperature and strain along an optical fiber by extracting the Brillouin frequency shift, and has important application value in power cables, oil and gas pipelines, bridges, tunnels, and extreme-environment monitoring. Conventional Brillouin optical time-domain analysis (BOTDA) and Brillouin optical time-domain reflectometry (BOTDR) generally rely on point-by-point frequency scanning to reconstruct the Brillouin spectrum. As a result, the measurement time is jointly limited by the number of scanning points and the averaging times, making it difficult to simultaneously achieve long sensing range and fast dynamic measurement. In recent years, the optical chirp chain (OCC) has provided a new idea for rapid distributed Brillouin sensing by establishing a time-frequency mapping relationship. Focusing on the two technical routes of OCC-BOTDA and OCC-BOTDR, this paper reviews the basic concept and implementation principle of OCC, as well as its research progress in ultrafast measurement, long-range and high-performance implementation, spectral distortion suppression, vector measurement and polarization enhancement, and single-end online demodulation. In addition, issues including parameter optimization, rapid demodulation, and multi-parameter sensing are discussed, together with future development directions.