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Manual video analysis is apparently a tedious task. An efficient solution is of highly importance to automate the process and to assist operators. A major goal of video analysis is understanding and recognizing human activities captured by surveillance cameras, a very challenging problem; the activities can be either individual or interactional among multiple objects. It involves extraction of relevant spatial and temporal information from visual images. Most video analytics systems are constrained by specific environmental situations. Different domains may require different specific knowledge to express characteristics of interesting events. Spatial-temporal trajectories have been utilized to capture motion characteristics of activities. The focus of this dissertation is on how trajectories are utilized in assist in developing video analytic system in the context of surveillance. The research as reported in this dissertation begins real-time highway traffic monitoring and dynamic traffic pattern analysis and in the end generalize the knowledge to event and activity analysis in a broader context. The main contributions are: the use of the graph-theoretic dominant set approach to the classification of traffic trajectories; the ability to first partition the trajectory clusters using entry and exit point awareness to significantly improve the clustering effectiveness and to reduce the computational time and complexity in the on-line processing of new trajectories; A novel tracking method that uses the extended 3-D Hungarian algorithm with a Kalman filter to preserve the smoothness of motion; a novel camera calibration method to determine the second vanishing point with no operator assistance; and a logic reasoning framework together with a new set of context free LLEs which could be utilized across different domains. Additional efforts have been made for three comprehensive surveillance systems together with main contributions mentioned above.