Inquisitive probing questions come naturally to humans in a variety of settings, but is a challenging task for automatic systems. One natural type of question to ask tries to fill a gap in knowledge during text comprehension, like reading a news article: we might ask about background information, deeper reasons behind things occurring, or more. Despite recent progress with data-driven approaches, generating such questions is beyond the range of models trained on existing datasets. We introduce INQUISITIVE, a dataset of ~19K questions that are elicited while a person is reading through a document. Compared to existing datasets, INQUISITIVE questions target more towards high-level (semantic and discourse) comprehension of text. We show that readers engage in a series of pragmatic strategies to seek information. Finally, we evaluate question generation models based on GPT-2 and show that our model is able to generate reasonable questions although the task is challenging, and highlight the importance of context to generate INQUISITIVE questions.