<p>The three-dimensional (3D) segmentation models for medical CT images assist the application of embodied AI in clinical medicine by providing precise anatomical information, thereby enhancing the accuracy and effectiveness of diagnostic and therapeutic interventions. Medical embodied AI currently faces five key challenges in clinical segmentation tasks: three-dimensional spatial consistency, precision, small-sample adaptability, generalizability, efficiency and intelligence. To address these specific challenges, convolutional neural network (CNN)-based models, Transformer-based models, and Segment Anything Model (SAM) extension models have been developed. This paper examines the latest advances in these models from both technical and application perspectives. From a technical perspective, it reviews the optimization strategies employed by the three types of 3D segmentation models to address various challenges. From an application perspective, it first analyzes the current practical applications of 3D segmentation models in embodied AI and subsequently forecasts their potential applications in light of clinical task requirements. Finally, the paper discusses prospective development directions for 3D segmentation models for medical CT imaging. Our work aims to inform researchers about the current progress in 3D segmentation models for medical CT images, critically review their applications in embodied AI, and promote their enhanced potential to assist medical embodied AI.</p>