Glenn died in December 2016 at the age of 95, after a long career that included serving as a Marine fighter pilot, a NASA astronaut and a US senator.
His five-hour solo orbit around Earth in 1962 established Glenn as an American pioneer. A year earlier, Russian cosmonaut Yuri Gagarin had become the first human in space and orbited the planet.
In 1998, Glenn made history again when he returned to space at the age of 77, becoming the oldest astronaut in space.
A Marine Corps honor guard folded a flag over his casket before it was lowered into the ground.
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President Donald Trump ordered all flags at government buildings in the United States and abroad to be flown at half-staff from sunrise to sundown "as a mark of respect for the memory of John Glenn."
Glenn was laid to rest on what would have been his 74th wedding anniversary. His wife, Annie, is 97.
"Senator Glenn was more than an astronaut -- he was the hero we needed in a rapidly changing world and an icon of our American spirit," said NASA administrator Robert Lightfoot in a statement.
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