As machines and agents become more autonomous, it has been increasingly clear to human factors/ergonomics researchers and practitioners that agent transparency is a critical issue for effective human-agent teaming. Transparency methods can provide the foundation for establishing shared awareness and shared intent between humans and intelligent machines. However, to date, the existing body of research on agent transparency has not been systematically documented. The purpose of this article is to summarize and evaluate current psychological theories and empirical evidence regarding effective agent transparency in human-autonomy teaming. We start by examining how transparency has been operationalized in the literature by discussing the two prominent theoretical frameworks of human-autonomy teaming. We then present a review of the empirical findings concerning how transparency affects key human-autonomy teaming variables, such as operator accuracy, decision time, situation awareness, perceived usability, and workload. This article includes an overview of the experimental tasks, scenarios, and interfaces that have been used in past studies and synthesizes how transparency has been operationalized and manipulated by prior studies. We then summarize the results and conclude by providing key recommendations for future research.