<p>The expansion of autonomous vehicle (AV) use in urban areas has motivated a range of studies aimed at addressing the diverse challenges arising in this field, particularly in recent years. This paper is a review of studies that investigate how traffic congestion has been addressed in routing problems within Autonomous Mobility-on-Demand (AMoD) systems since 2015, providing an integrated framework that organizes and synthesizes congestion-aware AMoD research. Given the limited number of studies in this field, the review includes not only research focused on autonomous systems, but also studies addressing shared ride services and those that incorporate traffic congestion in a simplified and indirect manner. In addition, works that assume static traffic conditions yet contribute to routing formulations and whose modeling approaches hold potential for further realistic development are considered. Moreover, studies that do not explicitly formulate a routing problem, but employ simulation tools for traffic modeling, are also included. Across the literature, it is observed that endogenous congestion feedback significantly alters routing, rebalancing, pricing, and welfare outcomes, while introducing calibration and computational burdens, thus highlighting that a hybrid approach would yield a valuable route for advances in this field.</p>