The physics and applications of fiber-based supercontinuum (SC) sources have been a subject of intense interest over the last decade, with a significant impact on both basic science and industry. New uses for SC sources are also constantly emerging due to their unique properties that combine high brightness, multi-octave frequency bandwidth, fiber delivery, and single-mode output. The last few years have seen significant research efforts focused on extending the wavelength coverage of SC sources towards the 2 to 20 μm molecular fingerprint mid-infrared (MIR) region and in the ultraviolet (UV) down to 100 nm, while also improving stability, noise, and coherence, output power and polarization properties. Here we review a selection of recent advances in SC generation in a range of specialty optical fibers including fluoride, chalcogenide, telluride, and silicon-core fibers for the MIR; UV-grade silica fibers, liquid-filled and gas-filled hollow-core fibers for the UV range; and all-normal dispersion fibers for ultra-low nose coherent SC generation.