The use of waste products in the production of asphalt binders and asphalt mixtures has become widespread due to economic and environmental benefits. In particular, the use of recycled waste plastic in asphalt binders and mixtures is gaining more attention. This review presents analyses and comparisons of various forms of waste plastic used in asphalt modification, and approaches to incorporating waste plastic into asphalt mixtures, both for single and composite modifications. It focuses on the properties of waste plastics, asphalt binders, and asphalt mixtures. Overall, the incorporation of plastic waste into asphalt mixtures can significantly improve high-temperature performance and has potential economic and environmental benefits. The performance of modified asphalt is highly dependent on multiple factors, such as waste sources, waste plastic dosages, blending conditions, and the pretreatment methods for waste plastic. There are different ways to apply waste plastics to blend into a mixture. In addition, this paper discusses the current challenges for waste plastic-modified asphalt, including the stability, low-temperature performance, modification mechanism, and laboratory problems of the blends. The use of chemical methods, such as additives and functionalization, is considered an effective way to achieve better interactions between waste plastics and the binder, as well as achieving a higher sufficiency utilization rate of waste plastics. Although both methods provide alternative options to produce waste plastic-modified asphalt with stability and high performance, the optimal proportion of materials used in the blends and the microcosmic mechanism of composite modified asphalt are not clear, and should be explored further.