Algorithmic decision-making increasingly shapes people's daily lives. Given that such autonomous systems can cause severe harm to individuals and social groups, fairness concerns have arisen. A human-centric approach demanded by scholars and policymakers requires considering people's fairness perceptions when designing and implementing algorithmic decision-making. We provide a comprehensive, systematic literature review synthesizing the existing empirical insights on perceptions of algorithmic fairness from 58 empirical studies spanning multiple domains and scientific disciplines. Through thorough coding, we systemize the current empirical literature along four dimensions: (1) algorithmic predictors, (2) human predictors, (3) comparative effects (human decision-making vs. algorithmic decision-making), and (4) consequences of algorithmic decision-making. While we identify much heterogeneity around the theoretical concepts and empirical measurements of algorithmic fairness, the insights come almost exclusively from Western-democratic contexts. By advocating for more interdisciplinary research adopting a society-in-the-loop framework, we hope our work will contribute to fairer and more responsible algorithmic decision-making.