Analogous to perfection in antiblocking theory is the notion of "the packing property" in blocking theory. A key insight on perfect graphs is the famous replication lemma proved by Laci Lovasz in 1972. In 1993, Michele Conforti and I proposed an analogous replication conjecture when the packing property holds. This conjecture is still open. This talk covers some recent developments related to the replication conjecture. These results are joint with Ahmad Abdi.