An overview of the progress on pulse-preserving, coherent, nonlinear fiber-based supercontinuum generation is presented. The context encompasses various wavelength ranges and pump sources, starting with silica photonic crystal fibers pumped with 1.0 μm femtosecond lasers up to chalcogenide step-index and microstructured fibers pumped from optical parametric amplifiers tuned to mid-infrared wavelengths. In particular, silica and silicate-based all-normal dispersion (ANDi) photonic crystal fibers have been demonstrated for pumping with femtosecond lasers operating at 1.56 μm with the recorded spectra covering 0.9–2.3 μm. This matches amplification bands of robust fiber amplifiers and femtosecond lasers. The review therefore focuses specifically on this wavelength range, discussing glass and nonlinear fiber designs, experimental results on supercontinuum generation up to the fundamental limit of oxide glass fiber transmission around 2.8 μm, and various limitations of supercontinuum bandwidth and coherence. Specifically, the role of nonlinear response against the role of dispersion profile shape is analyzed for two different soft glass ANDi fibers pumped at more than 2.0 μm. A spatio-temporal interaction of the fundamental fiber mode with modes propagating in the photonic lattice of the discussed ANDi fibers is shown to have positive effects on the coherence of the supercontinuum at pump pulse durations of 400 fs. Finally, the design and development of graded-index, nanostructured core optical fibers are discussed. In such structures the arbitrary shaping of the core refractive index profile could significantly improve the engineering flexibility of dispersion and effective mode area characteristics, and would be an interesting platform to further study the intermodal interaction mechanisms and their impact on supercontinuum coherence for sub-picosecond laser pumped setups.