This thesis work focuses on technical developments in the field of superresolution fluorescence microscopy (SRM) and applications of SRM to probing the spatial organization of biological systems at the nanometer and single-molecule scales. Fluorescence microscopy has been a powerful and essential tool for analyzing biological structures and processes due to its noninvasiveness and high molecular specificity. The spatial resolution of conventional fluorescence microscopy, however, is limited to about 250 nm by the diffraction of light. In the last decade or so, a suite of SRM techniques such as stimulated emission depletion (STED) microscopy, photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), have been invented to circumvent the diffraction limited spatial resolution of fluorescence microscopy. Among these, PALM and STORM are both based on subdiffractive localization of single fluorescent molecules and are the primary technical basis of the present work.