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Shared Autonomous Vehicles (SAVs) are expected to have a transformative role in future transportation systems, by reducing vehicle ownership, helping in alleviating congestion, improving accessibility and traffic safety, and changing travel behavior and urban infrastructure. The potential introduction of SAVs in transportation systems has triggered the need of exploiting suitable tools for designing and planning SAV operations and services and assessing their impacts. An explicit category of such tools are agent-based models (ABMs), whose advantage in efficiently representing transportation systems with a fine level of detail, has allowed them to gain importance in modeling SAVs. This paper systematically reviews and organizes the current state-of-the-art on ABMs dealing with SAVs. The review is two-fold: first, the methodological aspects of exploiting ABMs in the context of SAV services and operations are analyzed and second, ABM-based findings on the anticipated impacts of SAVs to traffic, travel behavior, land uses, the environment and so on, are presented and discussed. The paper concludes with recommendations for future research on SAVs and other, potential ABM applications for that purpose. [ABSTRACT FROM AUTHOR]