Medical imaging is essential in healthcare to provide key insights into patient anatomy and pathology, aiding in diagnosis and treatment. Non-invasive techniques such as X-ray, Magnetic Resonance Imaging (MRI), Computed Tomography (CT), and Ultrasound (US), capture detailed images of organs, tissues, and abnormalities. Effective analysis of these images requires precise segmentation to delineate regions of interest (ROI), such as organs or lesions. Traditional segmentation methods, relying on manual feature-extraction, are labor-intensive and vary across experts. Recent advancements in Artificial Intelligence (AI) and Deep Learning (DL), particularly convolutional models such as U-Net and its variants (U-Net++ and U-Net 3+), have transformed medical image segmentation (MIS) by automating the process and enhancing accuracy. These models enable efficient, precise pixel-wise classification across various imaging modalities, overcoming the limitations of manual segmentation. This review explores various medical imaging techniques, examines the U-Net architectures and their adaptations, and discusses their application across different modalities. It also identifies common challenges in MIS and proposes potential solutions.