Large Language Models (LLMs) have revolutionized natural language processing, yet their deployment is hindered by data, computation, and privacy constraints. Federated Learning (FL) offers a promising solution by enabling collaborative, privacy-preserving training across distributed devices, while the push for low-latency on-device intelligence further drives LLM integration into FL and edge settings—posing new challenges in heterogeneity and resource limits. This survey comprehensively reviews the integration of LLMs with federated learning, termed FLM, and its deployment at the edge, with particular emphasis on the robustness, privacy, and trustworthiness challenges that emerge across th... More >