In recent years, Event-based social network (EBSN) applications, such as Meetup and DoubanEvent, have received popularity and rapid growth. They provide convenient online platforms for users to create, publish, and organize social events, which will be held in physical places. Additionally, they not only support typical online social networking facilities (e.g., sharing comments and photos), but also promote face-to-face offline social interactions. To provide better service for users, Context-Aware Recommender Systems (CARS) in EBSNs have recently been singled out as a fascinating area of research. CARS in EBSNs provide the suitable recommendation to target users by incorporating the contextual factors into the recommendation process. This paper provides an overview on the development of CARS in EBSNs. We begin by illustrating the concept of the term context and the paradigms of conventional context-aware recommendation process. Subsequently, we introduce the formal definition of an EBSN, the characteristics of EBSNs, the challenges that are faced by CARS in EBSNs, and the implementation process of CARS in EBSNs. We also investigate which contextual factors are considered and how they are represented in the recommendation process. Next, we focus on the state-of-the-art computational techniques regarding CARS in EBSNs. We also overview the datasets and evaluation metrics for evaluation in this research area, and discuss the applications of context-aware recommendation in EBSNs. Finally, we point out research opportunities for the research community.