Anomaly detection in video surveillance is essential for maintaining safety in public spaces such as airports, train stations, and urban environments. This systematic review employs the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology to comprehensively analyze deep learning (DL)-based techniques for anomaly detection in urban video surveillance. Traditional methods, including trajectory-based and dictionary learning approaches, are compared against advanced DL techniques such as convolutional neural networks (CNNs), generative adversarial networks (GANs), and hybrid architectures. DL models demonstrate superior performance, achieving detection rates ranging from 68.4 to 99.83% across diverse datasets. This paper discusses key datasets, evaluation metrics, and real-world applications, emphasizing the strengths and limitations of various approaches. Challenges, including scalability, generalization, and ethical considerations, are also addressed, with a focus on privacy-preserving methods and multimodal data integration. The review concludes with future research directions, advocating for advancements in unsupervised learning, explainability, and adaptive frameworks to enhance the reliability and trustworthiness of DL-based anomaly detection systems. By highlighting both progress and gaps, this work provides a roadmap for developing robust and ethical anomaly detection solutions tailored to dynamic urban settings.