Epistemic curiosity is an affective state characterized by the desire for knowledge. This review paper suggests an integrative appraisal model of epistemic curiosity, which combines information-gap, emotion and reward-anticipation accounts of curiosity while proposing an appraisal theory-based explanation for why some knowledge gaps elicit curiosity. We discuss evidence for the involvement of brain circuits that support each step of curiosity-driven knowledge exploration. Overall, this integrative appraisal model of curiosity suggests that epistemic curiosity i) is an emotion which is triggered by appraised high relevance, valence, novelty and coping potential of knowledge-gaps; ii) confers a reward value to its epistemic object; iii) triggers a reward anticipation process; iv) and motivates a knowledge-seeking behavior (i.e., “wanting knowledge”). Once curiosity is satisfied, future knowledge-seeking expectations are updated according to affective prediction errors (i.e., “liking and learning”). If relevance is appraised as high but coping potential is appraised as low, the knowledge-gap rather creates anxiety and leads to information-avoidance. Future directions as to how this integrative model can be tested and extended are also discussed.