Fluorescence microscopy is a key driver of discoveries in the life-sciences, with observable phenomena being limited by the optics of the microscope, the chemistry of the fluorophores, and the maximum photon exposure tolerated by the sample. These limits necessitate trade-offs between imaging speed, spatial resolution, light exposure, and imaging depth. In this work we show how image restoration based on deep learning extends the range of biological phenomena observable by microscopy. On seven concrete examples we demonstrate how microscopy images can be restored even if 60-fold fewer photons are used during acquisition, how near isotropic resolution can be achieved with up to 10-fold under-sampling along the axial direction, and how tubular and granular structures smaller than the diffraction limit can be resolved at 20-times higher frame-rates compared to state-of-the-art methods. All developed image restoration methods are freely available as open source software in Python, FIJI, and KNIME.