Localization microscopy is a powerful tool for circumventing the diffraction limit in fluorescence microscopy. In this technique sparse subsets of the fluorophores labeling a sample are switched on and off, and subsequently localized with a precision on the order of several nanometers. A high resolution image can then be built up from the estimated positions. However, localization microscopy fundamentally produces a list of localizations rather than an image. This introduces a critical need for new quantitative image analysis methods that suit these data. This thesis describes several of these methods, which we have developed. The resolution in localization microscopy is not limited by diffraction. Instead we propose an image based resolution measure based on Fourier ring correlation (FRC). The FRC is both sensitive to the localization precision and the density of single fluorescent labels in a sample, as well as other factors such as the sample's spatial structure. We show how the FRC can be corrected for spurious correlations for acquisitions where the same molecules are localized several times. The FRC resolution provides a quantitative guide for the smallest details that can be reliably interpreted in images, thus enabling sound biological conclusions. Localization microscopy lacks a natural way of visualizing the data that are produced. Therefore we compare several proposed visualization methods, and show that the best FRC resolution is obtained by rendering localizations as Gaussian blobs whose widths are proportional to the corresponding localization precisions. Histogram binning provides a good alternative though, with only a slightly resolution in a shorter computation time. A major application of localization microscopy is the quantification of numbers of molecules in biological structures. However, the reversibly switchable fluorophores which are commonly used for imaging suffer from overcounting due to multiple localizations of the same molecule. Here we provide a method to estimate how often a marker such as an antibody is localized on average. The method makes use of the build-up of spurious correlations in the FRC during acquisition, and draws upon a model for the statistics of activation, bleaching, and labeling stoichiometry. Our method achieves a counting error of less than 20\% with single fluorophore labeled DNA oligomers and multiple-labeled Neutravidin tetramers, without any calibration of transition rates. When overcounting problems are resolved, incomplete labeling of the sample may result in undercounting problems instead. We address this issue for well-defined macromolecular complexes such as the nuclear pore complex (NPC). We show how the number of protein copies per subunit can be inferred by combining the localizations from multiple underlabeled complexes in a single statistical analysis. Co-localization analysis is a standard tool to probe multicolor fluorescence images for functional interactions between molecules in different channels. We extend this into the analysis of co-orientation: the combination of co-localization and orientational alignment of the structures on which the molecules reside. We employ this analysis to show that microtubuli exhibit statistically significant co-orientation with the intermediate filament vimentin in a cell-type specific manner. Together these methods substantially advance our ability to reliably and quantitatively interpret localization microscopy data and thereby enhances their utility for biological research.