The core of the big modern (relative term here given these designs are pretty old by now) bombs are implosion fission devices that then trigger a secondary fusion explosion. The core of that primary bomb is a plutonium ball called a pit that gets crushed to trigger the initial explosion. Then the xrays released by that get reflected and use in a secondary fusion device in the tiny amount of time the shell of the bomb lasts.
The pit (primary) is a hollow shape that gets crushed, producing a fission explosion. The X-rays released by that are absorbed by a (highly classified) foam encasing the secondary, which vaporizes (explodes), compressing the secondary causing fusion. The foam, and the secondary, are encased in a substantial tamper made of U-238.
The tamper’s mass impedes the expansion of the secondary, making it more efficient. The tamper is also largely converted to Pu-239 by the neutron flux from the secondary, and immediately fissions releasing a whole lot more energy. This approach is used in all modern thermonuclear weapons, with the majority of the total energy coming from fission.
The ‘Tsar Bomba’ weapon, the largest ever detonated, was designed to be a 100 megaton blast, but Khrushchev was concerned about fallout. So, he directed the U-238 tamper be replaced with lead, which reduced the explosive yield to ~60 MT.
