Large Language Models (LLMs) have had major impact in society even though most LLM applications use single model calls to generate output. Recent innovations have uncovered that multiple chained calls tend to produce better results. Even more impactful is the discovery that these chains do not need to be predefined. LLM-based AI agents use frameworks to generate written intermediate reasoning that decides which steps to take next and when to return with a final output. LLM-based AI agents can use external tools like search engines, calculators, code engines, etc. to gather information and act on the world. Developments in this area are rapid and potentially consequential. However, it is difficult to keep apace with the developments. To address this, we introduce a typology grounded in recent research that provides a structured framework for understanding LLM-based agents, facilitating proactive engagement with future developments.