The rapid development of artificial intelligence (AI) is not only a scientific breakthrough but also impacts on human society and economy as well as the development of economics. Research on AI economics is new and growing fast, with a current focus on the productivity and employment effects of AI. This paper reviews recent literature in order to answer three key questions. First, what approaches are being used to represent AI in economic models? Second, will AI technology have a different impact on the economy than previous new technologies? Third, in which aspects will AI have an impact and what is the empirical evidence of these effects of AI? Our review reveals that most empirical studies cannot deny the existence of the Solow Paradox for AI technology, but some studies find that AI would have a different and broader impact than previous technologies such as information technology, although it would follow a similar adoption path. Secondly, the key to incorporating AI into economic models raises fundamental questions including what the human being is and what the role of the human being in economic models is. This also poses the question of whether AI can be an economic agent in such models. Thirdly, studies on the labor market seem to have reached consensus on the stylized fact that AI would increase unemployment within sectors but may create employment gains at the aggregate level. AI also increases the income gap between low- and medium-skilled workers and high-skilled workers. AI’s impacts on international trade and education have been largely neglected in the current literature and are worth further research in the future.