Since the 1930s, polling organizations have asked Americans whether they “approve or disapprove of the job the incumbent is doing as president.” In the early 1970s, John Mueller started an academic industry by asking what drives these evaluations. American politics and the tools available to examine it have changed dramatically since then, inspiring a burst of research on presidential approval in the 1990s. We review this new body of literature, arguing that it builds on but differs importantly from earlier approval studies. Since Mueller’s writing, scholars have expanded his relatively simple model, taking account of presidents’ goals and personal characteristics, other political actors, the ubiquitous media, and an inattentive public. We describe three waves of research, focusing on the most recent wave. We suggest that history, along with new intellectual currents, data, and methods have enabled each wave to incorporate more of political, social, and psychological reality. Finally, we identify the issues most likely to motivate presidential approval research for the next ten years.