Machine-generated artworks are now part of the contemporary art scene: they are attracting significant investments and they are presented in exhibitions together with those created by human artists. These artworks are mainly based on generative deep learning (GDL) techniques, which have seen a formidable development and remarkable refinement in the very recent years. Given the inherent characteristics of these techniques, a series of novel legal problems arise. In this article, we consider a

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... of key questions in the area of GDL for the arts, including the following: is it possible to use copyrighted works as training set for generative models? How do we legally store their copies in order to perform the training process? Who (if someone) will own the copyright on the generated data? We try to answer these questions considering the law in force in both the United States and the European Union, and potential future alternatives. We then extend our analysis to code generation, which is an emerging area of GDL. Finally, we also formulate a set of practical guidelines for artists and developers working on deep learning generated art, as well as some policy suggestions for policymakers.