Decoupling theorem and effective quantum gravity

This is a contribution to the memorial edition devoted to Professor Vladislav Gavrilovich Bagrov, who was my official adviser from the beginning of undergraduate period to the end of Ph.D. The text includes a mentioning of two my publications in Izvestia VUZov Fisica (Russian Physics Journal), where Vladislav Gavrilovich served as an Editor. The rest of this paper is based on the recent lectures about decoupling in quantum gravity, given in ICTP-SAIFR in Sao Paulo and at the school ``Estate Quantistica'' in Scalea, Italy. After a brief and mainly qualitative review of the decoupling theorem in semiclassical gravity and the scalar fourth-derivative model of Antoniadis and Mottola, we explain what is the expected result for the physical beta functions in fourth-derivative quantum gravity and what should remain from these beta functions in the IR.