The current advances in Artificial Intelligence are likely to have profound economic implications and bring about new trade-offs, thereby posing new challenges from a policymaking point of view. What is the socio-economic impact of these new technologies on growth, employment and inequality? How markets and competition will be affected by AI-powered agents? What are the implications in terms of consumers' privacy? Will algorithms reduce consumers' biases or will they rather originate new ones? This work presents a first attempt to provide a comprehensive survey of the growing economic literature on Artificial Intelligence and its economic impact on markets and society, focusing on those issues where AI is likely to pose the most imminent challenges for policymakers.