Medical image segmentation provides detailed mappings of regions of interest, facilitating precise identification of critical areas and greatly aiding in the diagnosis, treatment, and understanding of diverse medical conditions. However, conventional techniques frequently rely on hand-crafted feature-based approaches, posing challenges when dealing with complex medical images, leading to issues such as low accuracy and sensitivity to noise. Recent years have seen substantial research focused on the effectiveness of deep learning models for segmenting medical images. In this study, we present a comprehensive review of the various deep learning-based approaches for medical image segmentation and provide a detailed analysis of their contributions to the domain. These methods can be broadly categorized into five groups: CNN-based methods, Transformer-based methods, Mamba-based methods, semi-supervised learning methods, and weakly supervised learning methods. Convolutional Neural Networks (CNNs), with their efficient feature self-learning, have driven major advances in medical image segmentation. Subsequently, Transformers, leveraging self-attention mechanisms, have achieved performance on par with or surpassing Convolutional Neural Networks. Mamba-based methods, as a novel selective state-space model, are emerging as a promising direction. Furthermore, due to the limited availability of annotated medical images, research in weakly supervised and semi-supervised learning continues to evolve. This review covers common evaluation methods, datasets, and deep learning applications in diagnosing and treating skin lesions, hippocampus, tumors, and polyps. Finally, we identify key challenges such as limited data, diverse modalities, noise, and clinical applicability, and propose future research in zero-shot segmentation, transfer learning, and multi-modal techniques to advance the development of medical image segmentation technology.