After a number of AI-winters, AI is back with a boom. There are concerns that it will disrupt society. The immediate concern is whether labor can win a ‘race against the robots’ and the longer-term concern is whether an artificial general intelligence (super-intelligence) can be controlled. This paper describes the nature and context of these concerns, reviews the current state of the empirical and theoretical literature in economics on the impact of AI on jobs and inequality, and discusses the challenge of AI arms races. It is concluded that despite the media hype neither massive jobs losses nor a ‘Singularity’ are imminent. In part, this is because current AI, based on deep learning, is expensive and difficult for (especially small) businesses to adopt, can create new jobs, and is an unlikely route to the invention of a super-intelligence. Even though AI is unlikely to have either utopian or apocalyptic impacts, it will challenge economists in coming years. The challenges include regulation of data and algorithms; the (mis-) measurement of value added; market failures, anti-competitive behaviour and abuse of market power; surveillance, censorship, cybercrime; labor market discrimination, declining job quality; and AI in emerging economies.