We present a detailed overview of stimulated Brillouin scattering (SBS) in single-mode optical fibers. The review is divided into two parts. In the first part, we discuss the fundamentals of SBS. A particular emphasis is given to analytical calculation of the backreflected power and SBS threshold (SBST) in optical fibers with various index profiles. For this, we consider acousto-optic interaction in the guiding geometry and derive the modal overlap integral, which describes the dependence of the Brillouin gain on the refractive index profile of the optical fiber. We analyze Stokes backreflected power initiated by thermal phonons, compare values of the SBST calculated from different approximations, and discuss the SBST dependence on the fiber length. We also review an analytical approach to calculate the gain of Brillouin fiber amplifiers (BFAs) in the regime of pump depletion. In the high-gain regime, fiber loss is a nonnegligible effect and needs to be accounted for along with the pump depletion. We provide an accurate analytic expression for the BFA gain and show results of experimental validation. Finally, we review methods to suppress SBS including index-controlled acoustic guiding or segmented fiber links. The second part of the review deals with recent advances in fiber-optic applications where SBS is a relevant effect. In particular, we discuss the impact of SBS on the radio-over-fiber technology, enhancement of the SBS efficiency in Raman-pumped fibers, slow light due to SBS and SBS-based optical delay lines, Brillouin fiber-optic sensors, and SBS mitigation in high-power fiber lasers, as well as SBS in multimode and microstructured fibers. A detailed derivation of evolutional equations in the guided wave geometry as well as key physical relations are given in appendices.
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