Super-Resolution Microscopy Techniques in the Neurosciences presents the new techniques that achieve resolution beyond the diffraction limit by using nonlinear optical effects and new conditions outside of the conditions that Abbe stipulated in 1973. The theoretical basis of each technique, its implementation in instrumentation and mathematical algorithms, its limiting assumptions, as well as a variety of key applications are all comprehensively described and critically discussed. In particular the problems and the limitations of each technique are carefully evaluated to a degree that was previously unknown in the literature. The key problems of probe development, specimen preparation, light damage to both the probe and the specimen, photon detector design and construction, mathematical algorithms used in the calculations, instrument control systems, specimen mechanical positional stability during the duration of the imaging process, and the control and mitigation of optical aberrations are faithfully discussed. Once the final composite or computed images are obtained, there are the confounding problems of image interpretation and analysis. These problems of image interpretation and the role of artifacts, both specimen and instrumentation derived, have always plagued optical microscopy and they still continue to do so.