The U-shaped network is one of the end-to-end convolutional neural networks (CNNs). In electron microscope segmentation of ISBI challenge 2012, the concise architecture and outstanding performance of the U-shaped network are impressive. Then, a variety of segmentation models based on this architecture have been proposed for medical image segmentations. We present a comprehensive literature review of U-shaped networks applied to medical image segmentation tasks, focusing on the architectures, extended mechanisms and application areas in these studies. The aim of this survey is twofold. First, we report the different extended U-shaped networks, discuss main state-of-the-art extended mechanisms, including residual mechanism, dense mechanism, dilated mechanism, attention mechanism, multi-module mechanism, and ensemble mechanism, analyze their pros and cons. Second, this survey provides the overview of studies in main application areas of U-shaped networks, including brain tumor, stroke, white matter hyperintensities (WMHs), eye, cardiac, liver, musculoskeletal, skin cancer, and neuronal pathology. Finally, we summarize the current U-shaped networks, point out the open challenges and directions for future research.