This article provides a comprehensive survey on fairness-aware recommender systems. As information filtering services, recommender systems have extremely enriched our daily life by providing personalized suggestions and facilitating people in decision-making, which makes them vital and indispensable to human society in the information era. However, as people become more dependent on them, recent studies show that recommender systems potentially own unintentional impacts on society and individuals because of their unfairness (e.g., gender discrimination in job recommendations).