Metacognition is a foundational component of intelligence that has become increasingly recognized as a cornerstone of capable, transparent AI systems. While LLMs have made significant progress, it remains unclear when, how, or to what extent they can exhibit or be endowed with effective metacognitive abilities, and 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 systematic, comprehensive review of the current state of knowledge on metacognition for LLMs. See the GitHub repo for the full paper list!