The basic concept, waveform construction, and time-frequency mapping mechanism of the optical chirp chain (OCC) are introduced, and the fundamental principle by which OCC improves the acquisition efficiency of Brillouin spectra is elucidated. The operating principles of optical chirp chain Brillouin optical time-domain analysis (OCC-BOTDA) and optical chirp chain Brillouin optical time-domain reflectometry (OCC-BOTDR) are described. Research advances in OCC-BOTDA are reviewed in terms of single-shot ultrafast measurement, long-range and high-performance sensing, suppression of transient effects and spectral distortions, vector measurement, polarization diversity, and denoising enhancement. Progress in OCC-BOTDR is summarized with respect to single-ended online demodulation and sensing-performance improvement. The measurement range, spatial resolution, measurement time, and other performance parameters of different approaches are comparatively analyzed. Future directions for OCC-based fast distributed Brillouin sensing are discussed. Further advances are required in high-quality OCC generation, coherent detection, and digital signal processing. Moreover, OCC-based fast distributed Brillouin sensing can be integrated with other techniques to enable long-range, coordinated sensing of multiple physical parameters, while improving the engineering applicability and reliability of measurement systems to meet the demands of multiparameter monitoring in complex engineering environments.