A new generation of ultrafast and low-noise supercontinuum (SC) sources is currently emerging, driven by the constantly increasing demands of spectroscopy, advanced microscopy, and ultrafast photonics applications for highly stable broadband coherent light sources. In this Perspective, we review recent progress enabled by advances in nonlinear optical fiber design, detail our view on the largely untapped potential for noise control in nonlinear fiber optics, and present the noise fingerprinting technique for measuring and visualizing the noise of SC sources with unprecedented detail. In our outlook, we highlight how these SC sources push the boundaries for many spectroscopy and imaging modalities and focus on their role in the development of ultrafast fiber lasers and frequency combs with ultra-low amplitude and phase noise operating in the 2 μm spectral region and beyond in the mid-IR.