The proliferation of social networking services has resulted in a rapid growth of their user base, spanning across the world. The collective information generated from these online platforms is overwhelming, in terms of both the amount of content produced every moment and the diversity of topics discussed. The real-time nature of the information produced by users has prompted researchers to analyse this content, in order to gain timely insight into the current state of affairs. Specifically, the microblogging service Twitter has been a recent focus of researchers to gather information on events occurring in real time. This article presents a survey of a wide variety of event detection methods applied to streaming Twitter data, classifying them according to shared common traits, and then discusses different aspects of the subtasks and challenges involved in event detection. We believe this survey will act as a guide and starting point for aspiring researchers to gain a structured view on state-of-the-art real-time event detection and spur further research in this direction.