This survey explores Agentic Large Language Models (LLMs), defining them as systems capable of reasoning, acting, and interacting to achieve goals. The authors organize research into three core categories: reasoning techniques like self-reflection and Chain of Thought; acting through tool use and robotics; and interaction within multi-agent simulations. The paper highlights how these capabilities form a virtuous cycle that generates new training data and improves performance. Additionally, it outlines a research agenda addressing critical challenges in safety, ethics, and reliability as LLMs evolve into autonomous assistants for domains like science and medicine.