Single molecule localization microscopy is a powerful tool that delivers high contrast and imaging specificity at a resolution beyond that of conventional microscopes. To obtain a super-resolved image, one needs to image at least hundred thousand camera frames and estimate the position of millions of molecules with nanometer precision. The tremendous amount of data that needs to be analyzed is one of the challenges scientists face when applying single molecule localization techniques. For this reason, a maximum likelihood estimation method is proposed in this thesis that attains the Cramer-Rao Lower Bound and estimates the position of single molecules in parallel on a GPU to achieve near real-time processing with high precision. A major drawback of current methods that detect single molecules is that the number of false positives is unknown. Therefore, a generalized likelihood ratio test is proposed here, which can control both the number of false positives and true positives withminimal user input. This target is stably achieved in the experiment over a large range of signal to background conditions. A key application of single molecule localization microscopy can be found in in vivo RNA imaging. In this thesis two RNA studies are presented: i) The nuclear pore complex structures and the kinetic interaction with mRNA are investigated, where a point mutation of mex67p triggered the nuclear export efficiency to drop significantly; and ii) A study on the mobility and occupation of mRNA within the nucleus is performed by instantaneously imaging the whole three-dimensional volume ofmRNAs in the nucleus of a living cell. Fromthis study, no evidence was obtained for exclusion or enrichment of the heterochromatin by mRNAs. For the general applicability of singlemolecule localization microscopy, the two-dimensionalmethods will need to be extended to three-dimensions. In threedimensional imaging small aberrations will become significant when imaging away from focus and therefore need to be compensated or calibrated. This thesis shows that one can extend single molecule localization into three-dimensions, or even a fourth-dimension such as color when the point spread function of a microscope is correctly distorted. Additionally, an adaptive optics strategy is presented that can correct for sample induced aberrations, and a method is proposed to encode emission color of the single molecule into the measurement.@en