Metacognition is a foundational component of intelligence critical to effective learning, problem solving, decision-making, communication, and more. In recent years, it has become increasingly recognized as a cornerstone of capable, transparent AI systems. Yet while LLMs have made significant progress across diverse real-world tasks, it is not yet clear when, how, or to what extent they can exhibit or be endowed with effective metacognitive abilities, nor how such abilities can be adapted to advance the fundamental capabilities, reliability, and intelligence of AI systems. This paper bridges this gap by presenting the first comprehensive overview of the current state of knowledge on metacognition for LLMs. We analyze and taxonomize the landscape of this emerging field and summarize recent technical advancements, including methods and benchmarks to measure and evaluate LLMs' metacognitive abilities, techniques to elicit, improve, and apply metacognition in LLMs, and findings and implications of ongoing research. We also discuss applications, open questions and challenges, and promising directions for future work. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful research and discussion. An organized list of papers can be found at https://github.com/yale-nlp/LLM-Metacognition.

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