We survey and clarify some recent appearances of the term ‘emergence’. We distinguish epistemological emergence, which is merely a limitation of descriptive apparatus, from ontological emergence, which should involve causal features of a whole system not reducible to the properties of its parts, thus implying the failure of part/whole reductionism and of mereological supervenience for that system. Are there actually any plausible cases of the latter among the numerous and various mentions of ‘emergence’ in the recent literature? Quantum mechanics seems to offer one, in the Bell properties of entangled particles, but other apparently promising candidates, such as non‐linear dynamical systems investigated by complexity studies and chaos theory, seem on careful analysis to display only epistemological emergence. We examine the consequences for physicalism of admitting ontological emergence in the micro‐physical.