Medical image segmentation represents a fundamental task in medical image analysis, serving as a critical component for accurate diagnosis, treatment planning, and disease monitoring. The emergence of Denoising Diffusion Probabilistic Models (DDPMs) has revolutionized the landscape of generative modeling and recently gained significant attention in medical image analysis. This comprehensive review examines the current state of the art in diffusion models for medical image segmentation, covering theoretical foundations, methodological innovations, computational efficiency strategies, and clinical applications. We analyze recent advances in latent diffusion frameworks, transformer-based architectures, and ambiguous segmentation modeling while addressing the practical challenges of implementing these models in clinical environments. The review encompasses applications across multiple medical imaging modalities including Magnetic Resonance Imaging (MRI), Computed Tomography (CT), ultrasound, and X-ray imaging, providing insights into performance achievements and identifying future research directions. Through systematic analysis of publications mostly from 2019 to 2025, we demonstrate that diffusion models have achieved remarkable progress in addressing fundamental challenges including data scarcity, inter-observer variability, and uncertainty quantification. Notable achievements include inference time being reduced from 91.23 s to 0.34 s for echocardiogram segmentation (LDSeg, Echo dataset), DSC scores up to 0.96 for knee cartilage MRI segmentation, and a +13.87% DSC improvement over baseline methods for breast ultrasound segmentation. This review serves as a comprehensive resource for researchers and clinicians interested in leveraging diffusion models for medical image segmentation, providing a roadmap for future research and clinical translation.