Developing efficient vessel-tracking algorithms is crucial for imaging-based diagnosis and treatment of vascular diseases. Vessel tracking aims to solve recognition problems such as key (seed) point detection, centerline extraction, and vascular segmentation. Extensive image-processing techniques have been developed to overcome the problems of vessel tracking that are mainly attributed to the complex morphologies of vessels and image characteristics of angiography. This paper presents a literature review on vessel-tracking methods, focusing on machine-learning-based methods. First, the conventional machine-learning-based algorithms are reviewed, and then, a general survey of deep-learning-based frameworks is provided. On the basis of the reviewed methods, the evaluation issues are introduced. The paper is concluded with discussions about the remaining exigencies and future research.