Artificial intelligence and digital twins have become more popular in recent years and have seen usage across different application domains for various scenarios. This study reviews the literature at the intersection of the two fields, where digital twins integrate an artificial intelligence component. We follow a systematic literature review approach, analyzing a total of 149 related studies. In the assessed literature, a variety of problems are approached with an artificial intelligence-integrated digital twin, demonstrating its applicability across different fields. Our findings indicate that there is a lack of in-depth modeling approaches regarding the digital twin, while many articles focus on the implementation and testing of the artificial intelligence component. The majority of publications do not demonstrate a virtual-to-physical connection between the digital twin and the real-world system. Further, only a small portion of studies base their digital twin on real-time data from a physical system, implementing a physical-to-virtual connection.