The emergence of large language models (LLMs) has revolutionized artificial intelligence, offering unprecedented capabilities in reasoning, generalization, and zero-shot learning. These strengths open new frontiers in wireless communications, where increasing complexity and dynamics demand intelligent and adaptive solutions. This article explores the role of LLMs in transforming wireless systems across three key directions: adapting pretrained LLMs for communication tasks, developing wireless-specific foundation models to balance versatility and efficiency, and enabling agentic LLMs with autonomous reasoning and coordination capabilities. We highlight recent advances, practical case studies, and the unique benefits of LLM-based approaches over traditional methods. Finally, we outline open challenges and research opportunities, including multimodal fusion, collaboration with lightweight models, and self-improving capabilities, charting a path toward intelligent, adaptive, and autonomous wireless networks.