Abstract: The advancement of 5G mobile communication and internet of things (IoT) has facilitated the development of intelligent applications, but has also rendered these networks increasingly complex and vulnerable to various targeted attacks. Numerous anomaly detection models, particularly those utilizing deep learning technologies, have been proposed to monitor and identify network anomalous events. However, the implementation of these models poses challenges for network operators lacking expert knowledge of these black-box systems. In this study, we present a comprehensive review of current anomaly detection models and methods in the field of communication networks. We categorize these models into four methodological groups based on their underlying principles and structures, with particular emphasis on the role of recent promising large language models (LLMs) in the field of anomaly detection. Additionally, we provide a detailed discussion of the models in the following four application areas: network traffic monitoring, networking system log analysis, cloud and edge service provisioning, and IoT security. Based on these application requirements, we examine the current challenges and offer insights into future research directions, including robustness, explainability, and the integration of LLMs for anomaly detection.