Alright, let's talk physics! Presume that every thing I mention is actually caveated with "so far as unclassified understanding goes." Also, another caveat that I was an intern at a WMD non-proliferation group two decades ago, so my understanding was never perfect to begin with and time may be playing tricks on me.
So the Tsar Bomba was designed to be twice as large as it actually detonated. What the hell?
See, a thermonuclear bomb like this is (in the Teller-Ulam design) a three stage weapon: first, the primary (a regular atomic bomb, generally a sphere of plutonium that is imploded really fast) goes. The primary is a fission bomb, where a bunch of fissile material (Pu-239 or U-235- or technically U-233 but that's never been done at scale- Pu239 is easiest to isolate so its most common) is rapidly pushed together and generates a whole bunch of energy. This is what destroyed Hiroshima and Nagasaki, this is an "atomic bomb." This energy release comes from the chain reaction of atoms splitting: one U or Pu atom splits into a chain of daughter atoms and gives off a lot of energy- and extra neutrons which hit other atoms and cause them to split, setting off a chain reaction of energy release when enough U/Pu atoms are dense enough.
And then the energy from that release is directed into a bunch of fusionable material (probably lithium-deuteride) which causes those atoms to get so hot they start to fuse. And that fusion (like in the sun itself) gives off much more energy- as a rough estimate let's say something like 10x the amount of energy from the primary.
And then there is a third stage, the uranium tamper. You take some depleted uranium (U238- which is what is left behind when you pulled out all of the U235 from the natural uranium) and you direct the energy of the fusion into that. And that causes the U238 to do fission (which it won't do normally, unless you dump a whole lot of neutrons into it). This is, basically, doubling the amount of energy released. It's this uranium tamper- which is basically free, once you have an enrichment program up and running- which was replaced by lead in the Tsar Bomba test, so it only produced half the energy it could have.
As a note, fission turns out to be where most of the fallout is generated, and fusion doesn't generate a much fallout. The infamous "neutron bombs" of the 1970's and 1980's were a common name for basically, a thermonuclear bomb without that Uranium tamper (e.g. something like a Tsar Bomba but smaller) which produced very little fallout relative to its size. This worried some people, who thought that a conventional NATO-Warsaw Pact war might go nuclear if the West German government could be convinced to allow the use of such a bomb on their territory because it had less fallout. This also explains why the uranium tamper wasn't included on the Tsar Bomba test, because that would have produced absurd amounts of nuclear fallout.
Also as a general rule large bombs aren't very efficient, because you are destroying everything in a sphere volume: to double the radius of destruction you need to increase the energy by a factor of 8. Once Minuteman came along, and there were a thousand very accurate ICBM's available (and then Minuteman III which added MIRV's so quickly tripling that- and the Soviets responded with SS-11) it was more efficient use of the expensive fissile material to put more smaller warheads around, because the delivery systems were no longer the bottleneck.