The theme of this chapter is the parametric estimation of depth-of-reasoning models. The most popular depth-of-reasoning models are variants of the Level-k model and the cognitive hierarchy model. After describing these models, previous attempts at econometric estimation of them are surveyed. Then a number of estimation issues are addressed. Firstly, identification problems that arise when applying the models to certain 2-player games are discussed. This leads into a discussion of the applications to situations in which the strategy space is continuous. The most popular application is the beauty contest game. In this context, a number of other econometric issues are addressed, including dealing with censoring at the extremes of the strategy space. A number of post-estimation tools and the key assumption underlying levels of reasoning models that agents actually form specific beliefs, and best-respond are illustrated. We will consider methods for testing this assumption in a simple auction experiment.