Living polymerization was first described by Michael Szwarc in 1956. It is defined as a chain polymerization from which chain transfer and chain termination are absent. In the absence of chain-transfer and chain termination, the monomer in the system is consumed and the polymerization stops but the polymer chain remains active. If new monomer is added, the polymerization can proceed. 
Due to the low PDI and predictable molecular weight, living polymerization is at the forefront of polymer research. It can be further divided into living free radical polymerization, living ionic polymerization and living ring-opening metathesis polymerization, etc.