When people feel curious, they often seek information to resolve their curiosity. Reaching resolution, however, does not always occur in a single step but instead may follow the accumulation of information over time. Here, we investigated changes in curiosity over a dynamic information-gathering process and how these changes related to affective and cognitive states as well as behavior. Human participants performed an Evolving Line Drawing Task, during which they reported guesses about the drawings' identities and made choices about whether to keep watching. In Study 1, the timing of choices was predetermined and externally imposed, while in Study 2, participants had agency in the timing of guesses and choices. Using this dynamic paradigm, we found that even within a single information-gathering episode, curiosity evolved in concert with other emotional states and with confidence. In both studies, we showed that the relationship between curiosity and confidence depended on stimulus entropy (unique guesses across participants) and on guess accuracy. We demonstrated that curiosity is multifaceted and can be experienced as either positive or negative depending on the state of information gathering. Critically, even when given the choice to alleviate uncertainty immediately (i.e., view a spoiler), higher curiosity promoted continuing to engage in the information-gathering process. Collectively, we show that curiosity changes over information accumulation to drive engagement with external stimuli, rather than to shortcut the path to resolution, highlighting the value inherent in the process of discovery.