Fluorescence imaging methods that push or break the diffraction limit of resolution (approximately 200 nm) have grown explosively. These super-resolution nanoscopy techniques include: stimulated emission depletion (STED), Pointillism microscopy [(fluorescence) photoactivation localization microscopy/stochastic optical reconstruction microscopy, or (F)PALM/STORM], structured illumination, total internal reflection fluorescence microscopy (TIRFM), and those that combine multiple modalities. Each affords unique strengths in lateral and axial resolution, speed, sensitivity, and fluorophore compatibility. We examine the optical principles and design of these new instruments and their ability to see more detail with greater sensitivity--down to single molecules with tens of nanometers resolution. Nanoscopes have revealed transient intermediate states of organelles and molecules in living cells and have led to new discoveries but also biological controversies. We highlight common unifying principles behind nanoscopy such as the conversion of a subset of probes between states (ground or excited) and the use of scanning (ordered or stochastic). We emphasize major advances, biological applications, and promising new developments.