Supercontinuum (SC) generation that leads to the emission of broadband radiation has been extensively studied. In particular, SC sources encompassing the wavelength range of 2–5 μm have attracted considerable interest in the last decade, and a continuous increase in the output power and spectrum width has been observed. To enable broadband and high-power SC generation, suitable nonlinear media combined with appropriate pump sources must be used, maintaining the output as spectrally flat. This paper briefly reviews the current state-of-the-art SC sources restricted to those based on fluoroindate fibers, including systems pumped with femtosecond, picosecond, and nanosecond pulses. First, the concept of SC generation in optical fibers is briefly presented. This is followed by an examination of indium fluoride optical fibers, with an emphasis on their material and waveguide properties. Furthermore, the advances in SC generation in fluoroindate fibers, including the latest results on high-power (Watt-level) continuum generation adopting different pump schemes, are also explored. A record time-averaged output power of 11.8 W with a spectrum spanning from ~1.9 to 4.9 µm has been demonstrated, which is certainly not the power limit of this technology. Finally, potential future directions of research are discussed at the end of this paper.