Intellectual property rights are fundamental to how economies organize innovation and steer the diffusion of knowledge. Copyright law, in particular, has developed constantly to keep up with emerging technologies and the interests of creators, consumers, and intermediaries of the different creative industries. We provide a synthesis of the literature on the law and economics of copyright in the digital age, with a particular focus on the available empirical evidence. First, we discuss the legal foundations of the copyright system and developments of length and scope throughout the era of digitization. Second, we review the literature on technological change with its opportunities and challenges for the stakeholders involved. We give special attention to empirical evidence on online copyright enforcement, changes in the supply of works due to digital technology, and the importance of creative re‐use and new licensing and business models. We then set out avenues for further research identifying critical gaps in the literature regarding the scope of empirical copyright research, the effects of technology that enables algorithmic licensing, and copyright issues related to software, data and artificial intelligence.