There is a lot of interest in providing detailed reports to schools indicating which skills pupils have mastered and which still need development -- and, more broadly, the knowledge, skills and understanding that pupils have acquired and not yet acquired. Cognitive diagnostic assessment is an approach designed to provide this kind of insight. Cognitive diagnostic assessment requires a detailed theory or model of the knowledge and skills to be measured, and how they relate to items. This theory then guides the assessment design, which may follow a formalised approach such as Evidence Centred Design (Mislevy et al., 2003) to ensure sufficiently robust validity. Cognitive diagnostic assessment then requires specific technical approaches to modelling and interpreting test-takers' responses. Cognitive Diagnostic Models (CDMs) -- also known as Diagnostic Classification Models (DCMs) -- are an important mainstream formal approach to this modelling. CDMs are a subset of multidimensional latent variable models, designed to "diagnose" students according to their mastery of the various skills or attributes being measured in a particular domain. The aim of this report is to give an up-to-date view on cognitive diagnostic models and what they might offer. In particular, it considers how assessment organisations could use CDMs to provide something of meaningful value to schools, and what would be required to make this work.