Colorectal cancer typically originates from the malignant transformation of colonic polyps, making the automatic and accurate segmentation of colonic polyps crucial for clinical diagnosis. Deep learning techniques such as U-Net and Transformer can effectively extract implicit features from medical images, and thus have significant potential in colonic polyp image segmentation. This paper first introduced commonly used evaluation metrics and datasets for colonic polyp segmentation. It then reviewed the application of segmentation models based on U-Net, Transformer, and their hybrid approaches in this domain. Finally, it summarized the improvement methods, advantages, and limitations of polyp segmentation algorithms, discussed the challenges faced by U-Net- and Transformer-based models, and provided an outlook on future research directions in this field.