The crumb-rubber-modified asphalt has attracted considerable attention owing to its excellent road service performance and low-carbon environmental protection characteristics. As studies focusing on expanding the applications of crumb-rubber-modified asphalts are limited, in this study, we systematically investigated the research trends of crumb-rubber-modified asphalts and their mixtures, different types of crumb rubber modified asphalts divided based on crumb rubber content. The preparation technology, modification mechanism and comprehensive performance of different types of crumb-rubber-modified asphalts and their mixtures were compared and evaluated, and based on the obtained mathematical statistics and relevant specifications, the performance grades of crumb-rubber-modified asphalts and their mixtures were divided. The results showed that the preparation of crumb-rubber-modified asphalt was mainly based on the high-speed shear method. With the increase in the crumb rubber content, the basic and rheological properties of the modified asphalt were significantly improved. However, problems emerged in the preparation of high-content crumb rubber asphalts, such as excessive viscosity and insufficient stability, excessive crumb rubber content can also hinder the compaction of the mixture and reduce its water stability. In view of the current traffic development focused to environmental protection and quality improvement, increasing the content of crumb rubber and improving the workability and storage stability of crumb rubber asphalt or using crumb-rubber- and resin-polymer-composite-modified asphalts are further research directions of crumb-rubber-modified asphalt-related technologies.