How much should we fear that a president will break the law to pursue power—then use their office to avoid legal accountability? Political scientists studying the presidency have often overlooked the risk of what we here call a criminal president. Donald Trump's presidency spotlighted that risk and has begun to shift the field's focus toward not just presidential power but presidential constraints. We believe this shift should continue. In this review, we aim to set an agenda that makes the danger of a criminal president central to understanding the presidency more broadly. Situating the criminal presidency within wider questions about legal and constitutional constraints on presidential power, we emphasize the unique risks to democracy that a president unbound by law can pose. We call for a greater focus on the legal rules governing the executive branch—especially unitary executive ideas—and the policies needed to hold criminal presidents accountable.