The hydrogen bomb, also known as a staged thermonuclear weapon,
is indeed the successor to the atomic bomb as CrazyIvan has
noded above. It is not the only weapon type that uses fusion
reactions, however; see the boosted fission weapon for more. The
hydrogen bomb is also known as a fission-fusion-fission weapon
in some instances due to its design.  How does it work?  Glad
you asked. I'll try to expand on what's already been offered
here. The first thing you need to know about a fusion weapon of
any kind is that it has at its heart a plain ol' fission weapon,
aka atomic bomb. This is usually called the initiator or
trigger. This is because fusion reactions are incredibly hard to
start, and require enormous amounts of energy to coax them into
existence. The only way of doing that in the field, as it were,
without buildings full of energy storage and devices, is to use
an atomic bomb.  So at the core of the fusion device is a
fission device. There is a neutron reflector as well, just like
in a boosted-fission we