Over the past years the availability of devices that can be used to track moving objects---GPS systems, mobile phones, radio telemetry, surveillance cameras, RFID tags, and more---has increased dramatically, leading to an explosive growth in movement data. Objects being tracked range from animals and cars, to hurricanes, sports players, and suspected terrorists. This increase in data naturally led to a significant increase in the number of methods developed to extract knowledge from moving object data. The movement of animals, people, and vehicles is embedded in a geographic context. This context both enables and limits movement. For instance, cars move on roads and birds ride air currents. But people cannot walk on water and wolves cannot cross a river gorge. Most analysis algorithms for trajectories have so far ignored context: trajectories are analyzed in an otherwise empty space. This severely limits the applicability of algorithmic methods and has led to a growing gap between the work of algorithms researchers and the needs of practitioners. We aim to bridge this gap by developing definitions of and algorithms for context-aware trajectory analysis. We will develop efficient context-sensitive algorithms for fundamental analysis tasks, such as trajectory similarity, simplification, and segmentation. One important aspect of our work will be to develop appropriate models for (geographic) context. Formalizing our models and testing their validity will be an iterative process executed simultaneously with algorithm development and experimental evaluation on real-world trajectories of birds, pedestrians, and vessels.