Objective: In this article, I present the ideas and trends that have given rise to the use of cognitive architectures in human factors and provide a cognitive engineering–oriented taxonomy of these architectures and a snapshot of their use for cognitive engineering. Background: Architectures of cognition have had a long history in human factors but a brief past. The long history entails a 50-year preamble, whereas the explosion of work in the current decade reflects the brief past. Understanding this history is key to understanding the current and future prospects for applying cognitive science theory to human factors practice. Method: The review defines three formative eras in cognitive engineering research: the 1950s, 1980s, and now. Results: In the first era, the fledging fields of cognitive science and human factors emphasized characteristics of the dancer, the limited capacity or bounded rationality view of the mind, and the ballroom, the task environment. The second era emphasized the dance (i.e., the dynamic interaction between mental operations and task environment). The third era has seen the rise of cognitive architectures as tools for choreographing the dance of mental operations within the complex environments posed by human factors practice. Conclusions: Hybrid architectures present the best vector for introducing cognitive science theories into a renewed engineering-based human factors. Application: The taxonomy provided in this article may provide guidance on when and whether to apply a cognitive science or a hybrid architecture to a human factors issue.