Curiosity refers to the intrinsic desire of humans and animals to explore the unknown, even when there is no apparent reason to do so. Thus far, no single, widely accepted definition or framework for curiosity has emerged, but there is growing consensus that curious behavior is not goal-directed but related to seeking or reacting to information. In this review, we take a phenomenological approach and group behavioral and neurophysiological studies which meet these criteria into three categories according to the type of information seeking observed. We then review recent computational models of curiosity from the field of machine learning and discuss how they enable integrating different types of information seeking into one theoretical framework. Combinations of behavioral and neurophysiological studies along with computational modeling will be instrumental in demystifying the notion of curiosity.