The US has dropped a hydrogen bomb but only in testing scenarios and not for actual war.
Hydrogen bombs have been detonated but primarily in testing scenarios and not in actual war.
The first successful test of a hydrogen bomb was performed and conducted in 1952 by the United States as part of Operation Ivy.
The Soviet Union also followed with their own tests in 1953.
The hydrogen bomb tests by the Soviet Union and the United States involved large scale detonations to demonstrate the power of the hydrogen bombs but were not actually used in warfare.
The US test during operation ivy, code named "Mike," was conducted on November 1st 1952 at Enewetak Atol in the Marshall Islands.
The test was the first to use the Teller-Ulam design, which was a staged fusion device and was also a major milestone in development of thermonuclear weapons.
And then following the Soviet tests and the United States tests, other nations such as the United Kingdom as well as China and France also developed and tested out hydrogen bombs as well.
In 1961 the Soviet Union also conducted a test of the Tsar Bomba which was the largest and also most powerful nuclear weapon that was ever detonated.
And although despite these tests that were done the hydrogen bombs were never and have never been used in war or combat.
The development and the testing of these bombs and weapons were mainly driven by the Cold War and also the concept of nuclear deterrence in which the treat of massive retaliation is intended to prevent any aggression.
Although the existence of these powerful bombs and weapons also continues to remain a huge concern for global security and efforts are still ongoing to reduce nuclear stockpiles and prevent any proliferation.