Artificial Intelligence based on Deep Learning is opening new horizons in Biomedical research and promises to revolutionize the Microscopy field. Slowly, it now transitions from the hands of experts in Computer Sciences to researchers in Cell Biology. Here, we introduce recent developments in Deep Learning applied to Microscopy, in a manner accessible to non-experts. We overview its concepts, capabilities and limitations, presenting applications in image segmentation, classification and restoration. We discuss how Deep Learning shows an outstanding potential to push the limits of Microscopy, enhancing resolution, signal and information content in acquired data. Its pitfalls are carefully discussed, as well as the future directions expected in this field.