The increasing pervasiveness of location-acquisition technologies has enabled collection of huge amount of trajectories for almost any kind of moving objects. Discovering useful patterns from their movement behaviours can convey valuable knowledge to a variety of critical applications. In this light, we propose a novel concept, called gathering, which is a trajectory pattern modelling various group incidents such as celebrations, parades, protests, traffic jams and so on. A key observation is that these incidents typically involve large congregations of individuals, which form durable and stable areas with high density. In this work, we first develop a set of novel techniques to tackle the challenge of efficient discovery of gathering patterns on archived trajectory dataset. Afterwards, since trajectory databases are inherently dynamic in many real-world scenarios such as traffic monitoring, fleet management and battlefield surveillance, we further propose an online discovery solution by applying a series of optimization schemes, which can keep track of gathering patterns while new trajectory data arrive. Finally, the effectiveness of the proposed concepts and the efficiency of the approaches are validated by extensive experiments based on a real taxicab trajectory dataset.