Children's and adolescents' cognitive, affective, and behavioral states of engagement enhance or impede enjoyment of, and performance with, educational games. We propose a comprehensive model of engagement states and apply it to research on educational game development and research on the role of various aspects of engagement on game play and learning. Emphasis is placed on individual differences in attention, memory, motor speed and control, persistence, and positive and negative affect (approach/avoidance), and how these pertain to social cognitions regarding mathematics achievement. Our challenge is to develop educational games that are effective for a wide variety of student engagement states. (Contains 1 figure.)