Cyber-physical systems such as robots and intelligent transportation systems are heavy producers and consumers of trajectory data. Making sense of this data and putting it to good use is essential for such systems. When industrial robots, intelligent vehicles and aerial drones are intended to co-exist, side-by-side, with people in human-tailored environments safety is paramount. Safe operations require uncertainty-aware motion pattern recognition, incremental reasoning and rapid decision-making to manage collision avoidance, monitor movement execution and detect abnormal motion. We investigate models and techniques that can support and leverage the interplay between these various trajectory-based capabilities to improve the state-of-the-art for intelligent autonomous systems.