Thanks to the rapid evolution of technologies such as artificial intelligence, big data and the Internet of Things, smart cities are increasingly relying on real-time video surveillance to strengthen public safety. However, the continuous production of large quantities of video streams raises a crucial challenge: how to detect suspicious behaviors automatically and in real time, such as assaults or other offenses. This study proposes a systematic analysis of the publications published between 2018 and 2024, focusing on the methods, issues and progress related to the detection of anomalies in smart cities. We have identified and analyzed a corpus of 100 scientific publications from university databases such as ScienceDirect and Scopus, following a systematic methodology based on the use of specific keywords and logical operators. The study highlights recent advances in machine learning and deep learning for real-time video analysis, in particular in the detection of aggressive or abnormal behaviors. However, the very notion of anomaly remains vague and highly contextual, which makes it difficult to generalize detection systems. In conclusion, this work offers an overview of the state of the art and suggests avenues to guide future research towards more accurate, efficient and adaptive monitoring systems in smart cities.