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Understanding cell functions is the major goal of molecular biology, which intends to elucidate the interactions between biomolecules at a subcellular level. One of the widely used techniques in molecular biology is fluorescence microscopy, which offers high specificity and sensitivity at the submicrometer spatial scale but is limited by diffraction to about 200nm lateral resolution, which is insufficient for the observation of many molecular processes. During the last two decades several super-resolution techniques overcoming the diffraction limit have been developed. However, imaging samples in three dimensions (3D) at high speed remains a challenging and not yet resolved task. This thesis focuses on enhancing super-resolution imaging towards fast, live-cell and 3D imaging. Super-resolution optical fluctuation imaging (SOFI) is a technique based on the stochastic fluctuations of photoswitchable fluorescent markers. It possesses several unique features such as background reduction, capability of increased pixel grid generation, i.e. spatial oversampling, as well as tolerance and robustness to a wide range of photoswitching conditions. In this thesis SOFI was extended to perform 3D analysis. As a result, the resolution in all three spatial dimensions can be improved and the depth sampling increased. We present a novel design of a 3D fluorescence microscope capable of acquiring images of eight depth planes simultaneously. This design incorporates an image-splitting prism, a single optical element allowing to achieve in-depth image separation. The optical performance of the 3D microscope was described and experimentally verified. The simultaneous depth plane acquisition allows to fully exploit the 3D capabilities of SOFI while generating additional virtual depth planes. An algorithm for the extraction of switching kinetics of fluorescent markers is presented. Using appropriate imaging conditions, we demonstrate the applications of 3D SOFI on several examples of fixed and living cells. We also present the potential of the 3D microscope for phase retrieval in transparent samples.