Online Social networks have become an easy means of communication for users to share their opinion on various topics, including breaking news, public events, and products. The content posted by a user can influence or affect other users, and the users who could influence or affect a high number of users are called influential users. Identifying such influential users has a wide range of applications in the field of marketing, including product advertisement, recommendation, and brand evaluation. However, the users’ influence varies in different topics, and hence a tremendous interest has been shown towards identifying topic-based influential users over the past few years. Topic-level information in the content posted by the users can be used in various stages of the topic-based influential user detection (IUD) problem, including data gathering, construction of influence network, quantifying the influence between two users, and analyzing the impact of the detected influential user. This has opened up a wide range of opportunities to utilize the existing techniques to model and analyze the topic-level influence in online social networks. In this paper, we perform a comprehensive study of existing techniques used to infer the topic-based influential users in online social networks. We present a detailed review of these approaches in a taxonomy while highlighting the challenges and limitations associated with each technique. Moreover, we perform a detailed study of different evaluation techniques used in the literature to overcome the challenges that arise in evaluating topic-based IUD approaches. Furthermore, closely related research topics and open research questions in topic-based IUD are discussed to provide a deep understanding of the literature and future directions.