Over the past years the availability of devices that can be used to track moving objects – GPS satellite systems, mobile phones, and more – has increased dramatically, leading to an explosive growth in movement data. Naturally the goal is not only to track objects but also to extract information from the resulting data. We develop algorithms both for basic analysis tasks, such as clustering, and to answer questions from domain scientists. Our work encompasses both point trajectory data (cars, animals, …) and moving non-point objects (hurricanes, river networks, …). A particular focus are models and algorithms for data uncertainty and stability (small changes in the data should lead to small changes in the result).