Skin cancer is a major global disease whose main threat lies in the risk of rapid spread and remote metastasis, with melanoma being the most lethal type. Automated and accurate segmentation of skin lesions with the help of computer-aided diagnostic systems is clinically significant, not only providing critical information to physicians, but also significantly improving the segmentation accuracy. In order to gain a deeper understanding of the related technology, this study summarizes the latest research progress in this field. Traditional image segmentation algorithms and their advantages and disadvantages are first introduced, followed by a discussion of deep learning-based approaches, focusing on classical structures such as convolutional neural networks (CNN) and U-Net. For the widely used U-Net and its variant models, they are subdivided into segmentation methods based on multi-scale features, contextual information, attention mechanisms, and dual codecs, and the technical improvements of each type of methods are analyzed. Finally, the publicly available datasets of skin lesion images are sorted out and the experimental results of some typical algorithms are compared, and the technical challenges and future development directions are discussed in light of the current situation.