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Introduction: Mining Twitter streaming posts (i.e. tweets) to find events or the topics of interest has become a hot research problem. In the last decade, researchers have come up with various techniques like bag-of-words techniques, statistical methods, graph-based techniques, topic modelling approaches, NLP and ontology-based approaches, machine learning and deep learning methods for detecting events from tweets. Among these techniques, the graph-based technique is efficient in capturing the latent structural semantics in the tweet content by modelling word co-occurrence relationships as a graph and able to capture the activity dynamics by modelling the user-tweet and user-user interactions. Discussion: This article presents an overview of different event detection techniques and their methodologies. Specifically, this paper focuses on graph-based event detection techniques in Twitter and presents a critical survey on these techniques, their evaluation methodologies and datasets used. Further, some challenges in the area of event detection in Twitter along with future directions of research are presented. Conclusion: A Microblogging services and online social networking sites like Twitter provides a massive amount of valuable information on real-world happenings. There is a need for mining this information, which will help in understanding the social interest and effective decision making on various emergencies. However, event detection techniques need to be efficient in terms of time and memory and accurate for processing such voluminous, noisy and fastarriving information from Twitter.