Artificial Intelligence based on Deep Learning (DL) is opening new horizons in biomedical research and promises to revolutionize the microscopy field. It is now transitioning from the hands of experts in computer sciences to biomedical researchers. Here, we introduce recent developments in DL applied to microscopy, in a manner accessible to non-experts. We give an overview of its concepts, capabilities and limitations, presenting applications in image segmentation, classification and restoration. We discuss how DL shows an outstanding potential to push the limits of microscopy, enhancing resolution, signal and information content in acquired data. Its pitfalls are discussed, along with the future directions expected in this field.