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This paper reviews nonlinear optical-fiber designs for signal processing using optical Kerr effects. The requirements for designing nonlinear fibers are described first. Then, the design concept is discussed and design examples are shown to illustrate the tradeoffs among the different fiber properties such as effective area, dispersion, and attenuation. Furthermore, fiber designs with distributed Brillouin frequency shift to mitigate the effect of simulated Brillouin scattering (SBS) in nonlinear fibers are discussed in detail. An SBS-threshold increase of 7 dB over conventional nonlinear fibers is experimentally demonstrated.