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Soliton self-frequency shift (SSFS), a consequence of Raman self-pumping that continuously red-shifts a soliton pulse, has been widely studied recently for applications to fiber-based sources and signal processing. In this paper, the fundamentals of SSFS are reviewed. Various fiber platforms for SSFS (single-mode fiber, microstructured fiber, and higher order mode fiber) are presented and experimental SSFS demonstrations in these fibers are discussed. Observation of Cerenkov radiation in fibers exhibiting SSFS is also presented. A number of interesting applications of SSFS, such as wavelength-agile lasers, analog-to-digital conversion, and slow light, are briefly discussed.