In recent years, there has been a growing demand for eﬃcient recommender systems which track users’ preferences and recommend potential items of interest to users. In this talk, I will give a brief review about recommender systems, including its problem setup and challenges. Some existing approaches will be discussed in details, such as collaborative ﬁltering, content-based ﬁltering, matrix completion, and hybrid systems. I will also present a few recent developments to tackle the so-called ”cold start” problem by incorporating covariate information including user proﬁles and social networks. If time permits, some asymptotic results will also be discussed.