The hydrogen bomb (H-Bomb), is far more powerful and deadly than the atomic bomb that was dropped on Hiroshima and Nagasaki to end World War II. In 1950, President Harry Truman started a program to develop the H-Bomb and it became the major weapon of the Cold War, though it was never used.
Developed first by the United States of America, the viability of the H-bomb was proven with a massive detonation in 1952 by the USA on an atoll of the Marshall Islands in the Pacific Ocean. The H-bomb consists of the release of massive energy when hydrogen atoms are fused together at very high temperature and pressure to form helium nuclei. The scientists instrumental in its development were the Hungarian immigrant Edward Teller and Polish immigrant Stanislaw Ulam.
In 1953, the Soviet Union was the first to produce an explosion which made use of nuclear fusion, greatly alarming the United States which had hoped to retain its nuclear lead indefinitely. However, this Soviet device was a huge ground-based installation rather than a deliverable weapon. It was not a "true" fusion bomb because the main use of the fusion reaction was not to produce explosive energy, but to produce a neutron flux which had the effect of boosting the fission reaction. That is, most of the explosive energy came from nuclear fission. The Soviet Union later developed a bomb similar to the Teller-Ulam design, and its scientists claimed to have invented it independently of the American bomb.
Subsequently Great Britain, France and China have all developed their own hydrogen bombs, however the UK no longer posess weaponised material and have foresworn testing of the weapons. Negotiations between the US and Russia have also drastically cut both those nations' arsenals, although both retain very large nuclear stockpile. Israel is also widely suspected to maintain a small nuclear arsenal, though the government has never confirmed or denied these reports. This is known in Israel as the "policy of deliberate ambiguity". The US maintained a similar policy throughout the Cold War, whereby it would "Neither Confirm Nor Deny" the specific deployment of nuclear weapons. However, this differs from Israeli policy; Israel neither confirms or denies possessing nuclear weapons, while the U.S. policy merely did not disclose the specific locations of nuclear weapons.
Interestingly, the Japanese were the first 'victims' of the H-bomb. A fishing boat was near the site of a test, and the fishermen received a severe amount of radiation, returning home very sick. Their catch was unloaded and sent to the market, causing a slump in the fish market, as no-one knew which of the fish were contaminated and thus refrained from buying fish for a while. 
The Hydrogen Bomb works by using a shell of fissile material surrounding a hydrogen pellet. When the shell is detonated, a massive amount of pressure is exerted onto the hydrogen atoms, causing them to fuse into helium, and release energy.