Flags are flying at half mast across the United States as family, friends and fellow astronauts gathered in Ohio to remember Neil Armstrong, the first man to walk on the moon.
Four US Navy F-18 fighter jets flew in a solemn "missing man" formation over the funeral at a private Cincinnati golf club in honour of Armstrong, commander of the historic Apollo 11 mission, who died Saturday aged 82.
"Neil Armstrong's first step on the moon paved the way for others to be the 'first' to step foot on another planet," said Charles Bolden, head of the US space agency NASA.
"We have an obligation to carry on this uniquely American legacy," NASA cited Bolden, a former astronaut, as saying at the funeral.
"A grateful nation offers praise and salutes a humble servant who answered the call and dared to dream."
The late-morning funeral at the exclusive Camargo Club was by invitation only, reflecting Armstrong's own intensely private nature. A public memorial is planned for September 12 in Washington.
On Monday, President Barack Obama ordered that flags at all US government premises be lowered to half mast to mark Armstrong's funeral.
His order applied to the Stars and Stripes on top of the White House, all public buildings, military posts, naval stations and US naval ships at sea anywhere in the world, as well as at US embassies and consulates.
Armstrong, who grew up in rural Ohio and flew in the US Navy before joining the US space program, became a world hero when he set foot on the moon on July 20, 1969.
The Apollo 11 commander, who died of complications from cardiovascular surgery, was decorated by 17 countries and received a slew of US honours, but he was never comfortable with his fame and shied away from the limelight.
Earlier in Cincinnati, lunar astronauts James Lovell and Eugene Cernan helped launch a charity in Armstrong's honour at the Cincinnati Children's Hospital Medical Center.
Armstrong's family had already requested that in lieu of flowers, donations be made to the charity, known as the Neil Armstrong New Frontiers Initiative, which it founded.
Lovell was commander of the ill-fated Apollo 13 that aborted its mission and returned to Earth after an oxygen tank exploded in space, while Cernan was in December 1972 the last of the 12 men to have walked on the moon.
Both men attended the funeral, along with Apollo 8 astronaut Bill Anders, according to local news reports.
Writing in the Guardian newspaper, British-born NASA astronaut Piers Sellers said there was much in Armstrong for those in science, technology and aviation to admire and learn from.
"He was the best of the best. The man was a master," Sellers said.
"I know that he wanted to see people going back to the moon, and going elsewhere during his lifetime. Hopefully, that will happen sometime soon. He is really something for the rest of us to try and live up to."