Here, we report analysis and summary of research in the field of localization microscopy for optical imaging. We introduce the basic elements of super-resolved localization microscopy methods for PALM and STORM, commonly used both in vivo and in vitro, discussing the core essentials of background theory, instrumentation and computational algorithms. We discuss the resolution limit of light microscopy and the mathematical framework for localizing fluorescent dyes in space beyond this limit, including the precision obtainable as a function of the amount of light emitted from a dye, and how it leads to a fundamental compromise between spatial and temporal precision. The properties of a good dye are outlined, as are the features of PALM and STORM super-resolution microscopy and adaptations that may need to be made to experimental protocols to perform localization determination. We analyse briefly some of the methods of modern super-resolved optical imaging that work through reshaping point spread functions and how they utilize aspects of localization microscopy, such as stimulated depletion (STED) methods and MINFLUX, and summarize modern methods that push localization into 3D using non-Gaussian point spread functions. We report on current methods for analyzing localization data including determination of 2D and 3D diffusion constants, molecular stoichiometries, and performing cluster analysis with cutting-edge techniques, and finally discuss how these techniques may be used to enable important insight into a range of biological processes.
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