As the Cold War escalated, Soviet and U.S. nuclear strategies changed. The concept of mutually assured destruction (MAD) as a deterrent against hostilities was reinforced by fleets of strategic bombers armed with thermonuclear warheads. The largest of which was the Tsar Bomba.
The Tsar Bomba was never put into use though, it was too bulky for transit, and nuclear bombers were soon to be outmoded by ICBMs and MIRV weaponry.
An interesting throwback to this "one-upping" of U.S. military might comes from Russia's latest vacumm bomb, nicknamed the "Father of all Bombs" which bypassed the American MOAB (Massive Ordnance Air Burst) which was later dubbed the Mother of all Bombs.