The emerging topic of sequential recommender systems (SRSs) has attracted increasing attention in recent years. Different from the conventional recommender systems (RSs) including collaborative filtering and content-based filtering, SRSs try to understand and model the sequential user behaviors, the interactions between users and items, and the evolution of users’ preferences and item popularity over time. SRSs involve the above aspects for more precise characterization of user contexts, intent and goals, and item consumption trend, leading to more accurate, customized and dynamic recommendations. In this paper, we provide a systematic review on SRSs. We first present the characteristics of SRSs, and then summarize and categorize the key challenges in this research area, followed by the corresponding research progress consisting of the most recent and representative developments on this topic. Finally, we discuss the important research directions in this vibrant area.