The seven articles in this special issue are concerned with the challenges of assessing complex aspects of cognition in the domains of mathematics, reading, history, and science. Each describes the design of assessments and their interpretive use, with a particular focus on assessments closely tied to classroom instruction. Individually and collectively, they make valuable contributions, highlighting many conceptual and practical considerations that need to be addressed in designing and validating assessments of key aspects of mathematical, literary, scientific, and historical reasoning. The discussion presented in this article is divided into three parts. Part 1 presents three conceptual frames regarding the nature of assessment and assessment design, providing an interpretive language for discussing the seven articles. Part 2 applies these frames to the articles as a way to interpret the specifics of each case. Part 3 highlights challenges that remain in operationalizing and validating assessments of complex cognition.