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U-Net and its variants have showcased exceptional performance in the domain of breast medical image segmentation. By employing a fully convolutional network (FCN) structure for semantic segmentation, the symmetrical structure of U-Net offers remarkable flexibility and adaptability. It can be tailored to diverse image segmentation tasks and challenges by adjusting network depth and incorporating new modules, leaving a significant impact on subsequent network designs. This paper aims to delve into the application of U-shaped convolutional networks in breast medical image segmentation, categorizing and summarizing U-shaped convolutional networks used for this purpose in recent years. It outlines the widely used breast medical image datasets and evaluation metrics, discusses common data augmentation techniques, and provides a detailed introduction to the network structure of the U-Net model along with traditional segmentation methods for breast medical images. Furthermore, it summarizes the improvements made to the U-Net network structure for breast medical image segmentation, including modifications like residual structures, multi-scale features, dilation mechanisms, attention mechanisms, skip connection mechanisms, and integration with Transformers. Finally, it addresses the current challenges and problems encountered in breast medical image segmentation and offers insights into future research directions.