A common task in surveillance, scientific discovery and data cleaning involves monitoring routinely collected data for anomalous events. Detecting events in univariate time series data can be effectively accomplished using well-established techniques such as Box-Jenkins models, regression, and statistical quality control methods. In recent years, however, routinely collected data has become increasingly complex. At each time step, the data collected can consist of multivariate vectors and/or be spatial in nature. For instance, healthcare data used in disease surveillance often consists of multivariate patient records or spatially distributed pharmaceutical sales data. Consequently, new event detection algorithms have been developed that not only consider temporal information but also detect spatial patterns and integrate information from multiple spatio-temporal data streams. This tutorial will present algorithms for event detection, with a focus on algorithms dealing with multivariate temporal and spatio-temporal data. We will introduce event detection by providing a general formulation of the event detection problem and describing its unique challenges. In the first half of the tutorial, we will cover algorithms for detecting events in both univariate and multivariate temporal data. The second half will present methods for detecting events in spatio-temporal data, including several recently proposed multivariate approaches.