Newly developed scientific complementary metal-oxide semiconductor (sCMOS) cameras have the potential to dramatically accelerate data acquisition, enlarge the field of view and increase the effective quantum efficiency in single-molecule switching nanoscopy. However, sCMOS-intrinsic pixel-dependent readout noise substantially lowers the localization precision and introduces localization artifacts. We present algorithms that overcome these limitations and that provide unbiased, precise localization of single molecules at the theoretical limit. Using these in combination with a multi-emitter fitting algorithm, we demonstrate single-molecule localization super-resolution imaging at rates of up to 32 reconstructed images per second in fixed and living cells.