Superresolution imaging of biological structures provides information beyond the optical diffraction limit. One class of superresolution techniques uses the power of single fluorescent molecules as nanoscale emitters of light combined with emission control, variously described by the acronyms PALM/FPALM/STORM and many others. Even though the acronyms differ and refer mainly to different active-control mechanisms, the underlying fundamental principles behind these "pointillist" superresolution imaging techniques are the same. Circumventing the diffraction limit requires two key steps. The first step (superlocalization) is the detection and localization of spatially separated single molecules. The second step actively controls the emitting molecules to ensure a very low concentration of single emitters such that they do not overlap in any one imaging frame. The final image is reconstructed from time-sequential imaging and superlocalization of the single emitting labels decorating the structure of interest. The statistical, imaging, and active-control strategies for achieving superresolution imaging with single molecules are reviewed.