Very fast, reversible, polyethylene (PE) chain transfer or complex-catalysed "Aufbaureaktion" describes a "living" chain-growing process on a main-group metal or zinc atom; this process is catalysed by an organo-transition-metal or lanthanide complex. PE chains are transferred very fast between the two metal sites and chain growth takes place through ethylene insertion into the transition-metal- or lanthanide-carbon bond-coordinative chain-transfer polymerisation (CCTP). The transferred chains "rest" at the main-group or zinc centre, at which chain-termination processes like beta-H transfer/elimination are of low significance. Such protocols can be used to synthesise very narrowly distributed PE materials (M(w)/M(n)<1.1 up to a molecular weight of about 4000 g mol(-1)) with differently functionalised end groups. Higher molecular-weight polymers can be obtained with a slightly increased M(w)/M(n), since diffusion control and precipitation of the polymers influences the chain-transfer process. Recently, a few transition-metal- or lanthanide-based catalyst systems that catalyse such a highly reversible chain-growing process have been described. They are summarised and compared within this contribution.