Searching for information in a goal-directed manner is central for learning, diagnosis, and prediction. Children continuously ask questions to learn new concepts, doctors do medical tests to diagnose their patients, and scientists perform experiments to test their theories. But what makes a good question? What principles govern human information acquisition and how do people decide which query to conduct to achieve their goals? What challenges need to be met to advance theory and psychology of human inquiry? Addressing these issues, we introduce the conceptual and mathematical ideas underlying different models of the value of information, what purpose these models serve in psychological research, and how they can be integrated in a unified formal framework. We also discuss the conflict between short- and long-term efficiency of prominent methods for query selection, and the resulting normative and methodological implications for studying human sequential search. A final point of discussion concerns the relations between probabilistic (Bayesian) models of the value of information and heuristic search strategies, and the insights than can be gained from bridging different levels of analysis and types of models. We conclude by discussing open questions and challenges that research needs to address to build a comprehensive theory of human information acquisition.