Self-improving agents are a top research topic right now. This new survey is a good map of the area. (bookmark it) It splits recursive self-improvement into stages of autonomy. An agent first executes improvements someone else designed. Then it chooses its own improvement strategy, collects its own experience, adapts to new environments, and finally improves the process of improvement itself. That staging makes claims easier to check. When a paper says its agent is self-improving, you can ask which of these stages it actually automates. The survey also uses a Headroom-Closed Index to show where current LLMs fall short, and compares requirements across scientific discovery, embodied agents and software engineering. Paper: