In this chapter, we discuss theories, hypotheses, and key studies examining cognitive issues of interpreting. We specifically focus on relevant topics such as cognitive effort, accuracy, and memory in both simultaneous and consecutive interpreting. The chapter begins with an overview of the literature spanning from the 1960s to today. We review modeling theories of interpreting (e.g., the Effort Models, Gile 1995) and the role of working memory in interpreting processes. The chapter then transitions to discuss the several methodologies and experimental designs that are typically utilized in interpreting research. Finally, the concluding section of the chapter offers a critical look at state-of-the-art issues that are relevant to both scholars and practitioners and provides insight on the persisting gaps in the literature that merit future investigation.