Educators and educational institutions love games. The contemporary currency of student engagement, in fact, appears to be in all things “gamified.” But what are games exactly, and how do we understand different games genres and their suitability for educational contexts? Indeed, it turns out that defining games and game genres is actually very difficult. It’s also critical to understanding how to integrate games into our instruction and our classrooms as “pedagogies of engagement.” We discuss games and their possibilities for engaging students in “expansive play-learning." Expansive play encourages questioning, analyzing, collaborating, modeling solutions and examining models, implementing strategies and reflecting on our actions. All games we want to encourage our students to play.