Anomaly detection has emerged as a foundational capability for intelligent urban systems, surveillance infrastructures, and complex cyber-physical environments. As cities evolve into highly instrumented, data-intensive ecosystems, the ability to identify abnormal patterns in human movement, vehicular trajectories, and video streams has become essential for ensuring safety, efficiency, and resilience. This research article presents an extensive, theory-driven investigation into contemporary deep learning-based anomaly detection methods, with a particular emphasis on trajectory analysis and video surveillance in smart city contexts. Grounded strictly in the existing scholarly literature, the study synthesizes autoencoder-based models, variational and distributional approaches, attention-driven sequence modeling, and contextual anomaly detection frameworks. Rather than offering a superficial survey, the article develops a unified conceptual narrative that explains why these methods work, how they differ philosophically and technically, and what their implications are for real-world deployment. The methodology section elaborates on representation learning, temporal dependency modeling, and context discovery without relying on mathematical formalism, ensuring conceptual clarity. The results section interprets reported findings across studies in a descriptive and comparative manner, highlighting strengths, weaknesses, and performance trends. The discussion critically examines limitations related to data bias, interpretability, scalability, and ethical deployment, while also identifying promising research directions such as multimodal fusion and adaptive context modeling. The article concludes by arguing that anomaly detection should be understood not merely as a technical task but as a socio-technical capability central to the future of smart cities.