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Healthy brain functioning depends on balancing stable integration between brain areas for effective coordinated functioning, with bursts of desynchronisation to allow subsystems to reconfigure and express functional specialisation. Metastability, a concept originated in statistical physics and dynamical systems theory, has been proposed as a key signature that characterises this balance. Building on this principle, the neuroscience literature has employed markers of metastability to investigate various aspects of brain function including cognitive performance, healthy ageing, meditation, sleep, responses to pharmacological challenges, and to characterise psychiatric conditions or disorders of consciousness. However, this body of work often uses the notion of metastability heuristically, and sometimes inaccurately, making it hard for the uninitiated to navigate the vast literature, interpret findings, and foster further development of theoretical and experimental methodologies. In this paper we provide a comprehensive review of metastability and its applications in neuroscience, covering its scientific and historical foundations and the practical estimators used to estimate it in empirical data. We also provide a critical analysis of recent theoretical developments, clarifying common misconceptions and paving the road for future developments.