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Search tasks play an important role in the study and development of interactive information retrieval (IIR) systems. Prior work has examined how search tasks vary along dimensions such as the task’s main activity, end goal, structure, and complexity. Recently, researchers have been exploring task complexity from the perspective of cognitive complexity—related to the types (and variety) of mental activities required by the task. Anderson & Krathwohl’s two-dimensional taxonomy of learning has been a commonly used framework for investigating tasks from the perspective of cognitive complexity [1]. A&K’s 2D taxonomy involves a cognitive process dimension and an orthogonal knowledge dimension. Prior IIR research has successfully leveraged the cognitive process dimension of this 2D taxonomy to develop search tasks and investigate their effects on searchers’ needs, perceptions, and behaviors. However, the knowledge dimension of the taxonomy has been largely ignored. In this conceptual paper, we argue that future IIR research should consider both dimensions of A&K’s taxonomy. Specifically, we discuss related work, present details on both dimensions of A&K’s taxonomy, and explain how to use the taxonomy to develop search tasks and learning assessment materials. Additionally, we discuss how considering both dimensions of A&K’s taxonomy has important implications for future IIR research.