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Large volumes of streaming data are becoming increasingly available in business and industry due to the growing popularity of sensors and the Internet of Things (IoT). In order to save memory, edge computing is usually employed, which leads to the generation of event data, i.e., discrete observations occurring in continuous time. Event data are ubiquitous in many industrial applications, such as vibration data for predictive maintenance, and within network data, including computer networks and social network data. This project primarily focuses on studying event data, particularly on modelling and understanding how systems change over time in an online fashion, as well as developing models and algorithms for real-time anomaly detection in event data.