In this chapter, we provide a comprehensive and up-to-date review of cognitive diagnosis computer adaptive testing (CD-CAT). Similar to Cheng and Keng (Computerized adaptive testing in criterion-referenced testing. In Smith E, Stone G (eds) Applications of Rasch measurement in criterion-reference testing: practive analysis to score reporting. JAM Press, Maple Grove, 2009), which provided a flowchart for a typical CAT, we provide a typical CD-CAT flowchart. Compared to regular CAT, a key distinction is that in CD-CAT the goal is to obtain the latent mastery profile for each respondent in an efficient fashion, or alternatively to obtain both the latent mastery profile (formative) and the latent ability (summative) simultaneously. The former is referred to as single-purpose CD-CAT, and the latter dual-purpose CD-CAT. We discuss the main components of CD-CAT in this chapter. These components will be covered in the following order: starting rule, item selection strategies, stopping rule, scoring rule, and item bank development and more specifically online calibration.