Fluorescence microscopy in its various forms has become the dominant methodology in biological imaging. This dominance is due, in large part, to its single-molecule sensitivity and its exquisite selectivity using chemical, antibody, or genetic targeting of labels to molecules of interest. Diffraction-limited resolution limits of 200 nm axially and 500 nm laterally were established in the 1870s for optical microscopy, and were held firmly until recently. During the past decade, a variety of methods have emerged that have the potential to push past the diffraction limits of resolution by at least an order of magnitude into the realm of molecular dimensions, even in examinations of living cell structures. This article examines four such strategies in the rapidly evolving field of superresolution microscopy: near-field scanning optical microscopy, stimulated emission depletion microscopy, superresolution structured illumination microscopy, and photoactivation localization microscopy and its relative, stochastic optical reconstruction microscopy.