As 6G wireless systems evolve, growing functional complexity and diverse service demands are driving a shift from rule-based control to intent-driven autonomous intelligence. User requirements are no longer captured by a single metric (e.g., throughput or reliability), but by multi-dimensional objectives such as latency sensitivity, energy preference, computational constraints, and service-level requirements. These objectives may also change over time due to environmental dynamics and user-network interactions. Therefore, accurate understanding of both the communication environment and user intent is critical for autonomous and sustainably evolving 6G communications. Large language models (LLMs), with strong contextual understanding and cross-modal reasoning, provide a promising foundation for intent-aware network agents. Compared with rule-driven or centrally optimized designs, LLM-based agents can integrate heterogeneous information and translate natural-language intents into executable control and configuration decisions. Focusing on a closed-loop pipeline of intent perception, autonomous decision making, and network execution, this paper investigates agentic AI for the 6G physical layer and its realization pathways. We review representative physical-layer tasks and their limitations in supporting intent awareness and autonomy, identify application scenarios where agentic AI is advantageous, and discuss key challenges and enabling technologies in multimodal perception, cross-layer decision making, and sustainable optimization. Finally, we present a case study of an intent-driven link decision agent, termed AgenCom, which adaptively constructs communication links under diverse user preferences and channel conditions.