Recommender systems are one of the most successful applications of data mining and machine learning technology in practice. Academic research in the field is historically often based on the matrix completion problem formulation, where for each user-item-pair only one interaction (e.g., a rating) is considered. In many application domains, however, multiple user-item interactions of different types can be recorded over time.And, a number of recent works have shown that this information can be used to build richer individual user models and to discover additional behavioral patterns that can be leveraged in the recommendation process.In this work we review existing works that consider information from such sequentially-ordered useritem interaction logs in the recommendation process. Based on this review, we propose a categorization of the corresponding recommendation tasks and goals, summarize existing algorithmic solutions, discuss methodological approaches when benchmarking what we call sequence-aware recommender systems, and outline open challenges in the area. 1:2 M. Quadrana et al.detected patterns are then used to compute recommendations that match the preference profiles of individual users.In academic environments, the predominant problem abstraction is that of matrix completion where we are given a user-item rating matrix and the goal is to predict the missing values. This abstraction is generally well-suited to train machine learning models that aim to capture longer-term user preference profiles. The corresponding algorithms however typically implement no specific means to take the users' short-term behavior or intents into account in their recommendations; nor are they designed to use the rich information that is contained in the sequentially-ordered user interaction logs that are often available in practical applications.In practice, however, there are many application scenarios where considering short-term user interests and longer-term sequential patterns can be central to the success of a recommender. A typical example problem setting is that of session-based recommendation [45,56], where no longer-term user histories are available. Instead, we have to adapt the recommendations according to the assumed short-term interests of an anonymous user. The goal in such scenarios usually is to recommend objects that match a given sequence of user actions.Typical algorithmic approaches in that context learn to predict the best next item from sequential user interaction logs. Considering such sequences is however not only relevant for the short-term adaptation of the recommendations. The sequential logs can also be used to derive longer-term behavior patterns, e.g., to detect interest drifts of individual users over time [85], to identify shortterm popularity trends in the community that can be exploited by recommendation algorithms [54,62], or to reason about the best point in time to remind users of certain items they have seen or purchased before [70]. Finally, there are application domains where the recomm...