Language proficiency is multi-componential in nature and, according to many SLA researchers and L2 practitioners, is best captured by the concepts of complexity, accuracy, and fluency (CAF). Two of the three studies reported in this paper adopted the Cognition Hypothesis (Robinson, 2003) as the means to address the question of whether increasing task complexity positively impacts learning and performance. The Cognition Hypothesis claims that increasing cognitive task complexity along specific dimensions has the potential to promote "greater analysis, modifications, and restructuring of the IL (interlanguage) with consequent performance effects" (Robinson, 2001a, p. 302). The studies that invoke the Cognition Hypothesis either refer to Robinson's Triadic Framework (Robinson, 2001a) and the Cognition Hypothesis to structure their research and explain the findings, or they take a more radical stand to argue that the premises underlying the Cognition Hypothesis and the claims derived from it are problematic. This forum begins with a literature review on CAF. It then reports on metric indices employed in the studies to measure the phenomenon of linguistic complexity and the results pertaining to grammatical and lexical complexity. Next, it describes the status of theory in empirical research and the challenges research on CAF faces. The closing presents a discussion on how theory impacted the design of the empirical studies sampled for this paper.