With the growing popularity of microblogging services such as Twitter in recent years, an increasing number of users are using these services in their daily lives. The huge volume of information generated by users raises new opportunities in various applications and areas. Inferring user interests plays a significant role in providing personalized recommendations on microblogging services, and also on third-party applications providing social logins via these services, especially in cold-start situations. In this survey, we review user modeling strategies with respect to inferring user interests from previous studies. To this end, we focus on four dimensions of inferring user interest profiles: (1) data collection, (2) representation of user interest profiles, (3) construction and enhancement of user interest profiles, and (4) the evaluation of the constructed profiles. Through this survey, we aim to provide an overview of state-of-the-art user modeling strategies for inferring user interest profiles on microblogging social networks with respect to the four dimensions. For each dimension, we review and summarize previous studies based on specified criteria. Finally, we discuss some challenges and opportunities for future work in this research domain.