Optical fiber lasers and amplifiers based on stimulated Brillouin scattering (SBS) in optical fibers and their applications are reviewed. Due to their intrinsicly unique characteristics,fiber Brillouin amplifier (FBA) and Brillouin fiber laser (BFL) have important applications in many fields. In particular,researches on FBA-based optical slow light buffer,ultra-narrow line-width BFL,multi-wavelength BFL and optical generation of microwave signals based on BFL have been attracting much attention in recent years. Their latest advances are focused in this review. Because of its potential applications,SBS in optical fibers may play important roles in fields of future all-optical telecommunication systems,coherent optical transmission systems and optical fiber sensing.