U-net is an image segmentation technique developed primarily for image segmentation tasks. These traits provide U-net with a high utility within the medical imaging community and have resulted in extensive adoption of U-net as the primary tool for segmentation tasks in medical imaging. The success of U-net is evident in its widespread use in nearly all major image modalities, from CT scans and MRI to X-rays and microscopy. Furthermore, while U-net is largely a segmentation tool, there have been instances of the use of U-net in other applications. Given that U-net's potential is still increasing, this narrative literature review examines the numerous developments and breakthroughs in the U-net architecture and provides observations on recent trends. We also discuss the many innovations that have advanced in deep learning and discuss how these tools facilitate U-net. In addition, we review the different image modalities and application areas that have been enhanced by U-net.