The process of knowledge acquisition can be viewed as a question-answer game between a student and a teacher in which the student typically starts by asking broad, open-ended questions before drilling down into specifics (Hintikka, 1981; Hakkarainen and Sintonen, 2002). This pedagogical perspective motivates a new way of representing documents. In this paper, we present SQUASH (Specificity-controlled Question-Answer Hierarchies), a novel and challenging text generation task that converts an input document into a hierarchy of question-answer pairs. Users can click on high-level questions (e.g., “Why did Frodo leave the Fellowship?”) to reveal related but more specific questions (e.g., “Who did Frodo leave with?”). Using a question taxonomy loosely based on Lehnert (1978), we classify questions in existing reading comprehension datasets as either GENERAL or SPECIFIC . We then use these labels as input to a pipelined system centered around a conditional neural language model. We extensively evaluate the quality of the generated QA hierarchies through crowdsourced experiments and report strong empirical results.