Social media platforms such as (Twitter, Facebook, and Weibo) are being increasingly embraced by individuals, groups, and organizations as a valuable source of information. This social media generated information comes in the form of tweets or posts, and normally characterized as short text, huge, sparse, and low density. Since many real-world applications need semantic interpretation of such short texts, research in Short Text Topic Modeling (STTM) has recently gained a lot of interest to reveal unique and cohesive latent topics. This article examines the current state of the art in STTM algorithms. It presents a comprehensive survey and taxonomy of STTM algorithms for short text topic modelling. The article also includes a qualitative and quantitative study of the STTM algorithms, as well as analyses of the various strengths and drawbacks of STTM techniques. Moreover, a comparative analysis of the topic quality and performance of representative STTM models is presented. The performance evaluation is conducted on two real-world Twitter datasets: the Real-World Pandemic Twitter (RW-Pand-Twitter) dataset and Real-world Cyberbullying Twitter (RW-CB-Twitter) dataset in terms of several metrics such as topic coherence, purity, NMI, and accuracy. Finally, the open challenges and future research directions in this promising field are discussed to highlight the trends of research in STTM. The work presented in this paper is useful for researchers interested in learning state-of-the-art short text topic modelling and researchers focusing on developing new algorithms for short text topic modelling.