Systems of "living" polymers are ubiquitous in industry and are traditionally realised using surfactants. Here I first review the theoretical state-of-the-art of living polymers and then 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.
Keywords: DNA; living polymers; non-equilibrium polymer physics; topology.