Behavioural monitoring often concerns the interpretation of the motion of an agent with respect to an area of interest. Geometrically, the trajectory of the agent is represented by a directed line segment (DLine) around/over a region. Topological relations between a DLine and a region concern how the DLine intersect with the region and, therefore, these relations are useful for characterizing the motion in association with an area of interest. In this chapter, we introduce a formal model of topological DLine-region relations and the application of these relations for the characterization of motions. We start from a model of topological relations between a non-directed line and a region, called the 9-intersection, reviewing how these line-region relations are associated with spatial predicates. Then, we introduce the 9⁺-intersection, which distinguishes 26 topological DLine-region relations in , with which we explore several approaches to associating motions with the model of human motion concepts. Finally, we introduce two future research questions: (i) simplification of complex trajectories by segmentation and (ii) mapping between non-planar motion concepts and topological DLine-region relations in .