Systems of “living” polymers are ubiquitous in industry and are traditionally realised using surfactants. Here I review the state-of-the-art of living polymers and discuss non-equilibrium extensions that may be realised with advanced synthetic chemistry or DNA functionalised by proteins. These systems are not only interesting in order to realise novel “living” soft matter but can also shed insight into how genomes are (topologically) regulated in vivo. ### Competing Interest Statement The authors have declared no competing interest.

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