Existing super-resolution fluorescence microscopes compromise acquisition speed to provide subdiffractive sample information. We report an analog implementation of structured illumination microscopy that enables three-dimensional (3D) super-resolution imaging with a lateral resolution of 145 nm and an axial resolution of 350 nm at acquisition speeds up to 100 Hz. By using optical instead of digital image-processing operations, we removed the need to capture, store and combine multiple camera exposures, increasing data acquisition rates 10- to 100-fold over other super-resolution microscopes and acquiring and displaying super-resolution images in real time. Low excitation intensities allow imaging over hundreds of 2D sections, and combined physical and computational sectioning allow similar depth penetration to spinning-disk confocal microscopy. We demonstrate the capability of our system by imaging fine, rapidly moving structures including motor-driven organelles in human lung fibroblasts and the cytoskeleton of flowing blood cells within developing zebrafish embryos.