This paper aims to identify the utility of and the need for cognitively diagnostic assessments (CDAs) in conjunction with cognitive diagnosis models (CDMs), and to outline various considerations involved in their development and use. We begin by contrasting the CDA/CDM framework against existing assessment frameworks, which are typically based on item response theory or classical test theory, and show that CDAs used in the CDM context can provide valuable diagnostic information that could enhance classroom instruction and learning. We then detail how the components of a CDA fit into the assessment triangle framework, as well as the evidence-centered design framework. Attribute identification and item development in the context of CDA are discussed, and examples from relevant research are provided. Details of CDMs, which are the statistical models that underpin the practical implementations of CDAs, are also discussed.