He did it from the moon.
With that, the Apollo 11 astronaut stepped off the "Eagle" lunar module and became the first man to walk on a planet or planetoid other than the earth. He was joined by crew mate Buzz Aldrin, while astronaut Michael Collins remained in the orbiter above the moon.
Armstrong piloted the Eagle landing craft to the surface manually, while the spacecraft's computer sounded alarms: NASA says on its Web site that the computer was trying to handle too many tasks at once.
"[Armstrong] felt that the chances of a successful landing [were] about 50-50," Armstrong biographer James Hansen told CBS News this week.
At the landing site, Armstrong and Aldrin left behind an American flag, a patch honoring the fallen Apollo 1 crew, and a plaque on one of Eagle's legs. It reads, "Here men from the planet Earth first set foot upon the moon. July 1969 A.D. We came in peace for all mankind."
Over the next three-and-a-half years, 10 more astronauts followed in their footsteps, but no one has visited the moon since 1973.
President Bush earlier this year set a goal of returning to the moon by 2020.
He has proposed developing a new spacecraft to carry Americans to the moon and to establish a long-term base there as a springboard to Mars and beyond.
A new Gallup Poll shows two-thirds of Americans say the U.S. should go back to the Moon; The numbers are slightly higher in orbit:
"A recent poll of the residents of the international space station is 100 percent of us would like to go back to the moon," American astronaut Mike Fincke told CBS News.
Thirty-five years after the space race between their countries ended, Fincke and Russian roommate Gennady Padalka have congratulated the Apollo Eleven crew.
"Our best wishes are with them and thank you for blazing the path," Fincke said.
Armstrong mostly has kept out of the public eye for the past 35 years, concentrating on being a professor at the University of Cincinnati, reports CBS News Correspondent Peter King.
But the normally low profile Armstrong is working with Auburn University's Hansen on what Hansen calls an atypical authorized biography.
"Neil was emphatic: He wanted it to be a critical, independent scholarly monograph," Hansen said.
It will be published next year by Simon and Schuster, which, like CBSNews.com, is a part of Viacom.
Armstrong doesn't do many interviews, but Hansen says he's done about 50 hours' worth with him, in part, to correct 35 years worth of stories he says got it all wrong.
"A lot of them are not true. They're apocryphal, they're made up, they're fabricated," Hansen said. For example, stories about Armstrong's childhood dreams of flying in space are a myth.
"His life was about flying, his life was about piloting," Hansen said.
Armstrong cared more about getting to the Moon, than he did about walking on it, the Auburn professor said.
"All of his focus for his entire career led him not to stepping off, it was about flying that LEM (landing module) down to the landing," Hansen told King.
"All of the attention that ... the public put on stepping down that ladder onto the surface itself, Neil never could really understand why there was so much focus on that," Hansen added.