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We report recent advances on the spectral control of continuous-wave-pumped supercontinuum sources. We show that the generated infrared SC spectrum can be tailored by using photonic crystal fibers with two zero-dispersion wavelengths. The dynamics of the spectral broadening is studied, and we show that slightly different nonlinear mechanisms occur as the zero-dispersion wavelengths are brought closer to each other. We also report the generation of a visible continuous-wave-pumped supercontinuum by using dispersion engineered photonic crystal fibers in which the zero-dispersion wavelength slightly decreases as a function of length over 200 m. The resulting supercontinuum source spans from 650 nm to 1380 nm with an average output power of 19.5 W. The nonlinear mechanisms producing this spectacular effect are carefully investigated with support of numerical simulations. We show that the generation of visible wavelengths is due to the trapping of dispersive waves by powerful red-shifting solitons.