Many machine learning applications depend on unauthorized uses of copyrighted training data. Scholars and lawmakers often articulate this problem as a deficiency in copyright’s exceptions and limitations. In fact, today’s predicament results not from inadequate exceptions to copyright, but rather from two systemic features of the regime—the absence of formalities and the low threshold of copyrightable originality—combined with technology that turns routine activities into acts of authorship. This chapter taxonomizes AI applications by their training data. Four categories emerge: (1) public-domain data, (2) licensed data, (3) market-encroaching uses of copyrighted data, and (4) non-market-encroaching uses of copyrighted data. Copyright can only regulate market-encroaching uses, but these uses comprise only a narrow subset of AI, and copyright’s remedies are ill-suited to address them. The chapter concludes with a discussion of solutions to the problems it identifies. It observes that the exception for Text and Data Mining in the European Union’s Directive on Copyright in the Digital Single Market represents a positive development because the exception addresses structural causes of AI’s copyright problems. The TDM provision styles itself as an exception, but it may be better understood as a formality: rights holders must affirmatively reserve the right to exclude materials from training datasets. Thus, the TDM exception addresses a cause of AI’s copyright dilemma. The next step for an equitable AI framework will be to transition towards rules that not only clarify that non-market-encroaching uses do not infringe copyright, but also facilitate remunerated uses of copyrighted works for market-encroaching purposes.