Recent advances in far-field microscopy have demonstrated that fluorescence imaging is possible at resolutions well below the long-standing diffraction limit. By exploiting photophysical properties of fluorescent probe molecules, this new class of methods yields a resolving power that is fundamentally diffraction unlimited. Although these methods are becoming more widely used in biological imaging, they must be complemented by suitable data analysis approaches if their potential is to be fully realized. Here we review the basic principles of diffraction-unlimited microscopy and how these principles influence the selection of available algorithms for data analysis. Furthermore, we provide an overview of existing analysis strategies and discuss their application.