This chapter introduces the subfield of player modeling, one the three constituent parts of AI and games as defined in this book. The chapter starts with laying out the various reasons for wanting to model game players, and defining player modeling by comparison with other tasks such as player imitation. This is followed by a comprehensive taxonomy of player modeling, focused on the role of the model, the methodological approach taken, and the types of input to the model and output from it. The discussion of methodological approaches introduces the distinction between top-down models, which are informed by theories from fields such as psychology, game studies, and neuroscience, and bottom-up theories which are purely driven by machine learning. Several theories of player experience are discussed in some detail.