National policy and standards documents, including the National Assessment of Educational Progress frameworks, the "Common Core State Standards" and the "Next Generation Science Standards," assert the need to assess critical-analytic thinking (CAT) across subject areas. However, assessment of CAT poses several challenges for developers of both large-scale and classroom assessments: Current CAT assessments often suffer from questionable item contexts, subjective rubrics, and underdeveloped construct formulations. Attention to these aspects of assessment would improve understanding of the development of students' CAT and provide tools for helping teachers teach and students learn. We discuss these challenges within the context of several content areas and highlight the importance of developing formative assessments that capture the development of CAT in different domains of learning.