* US President Barack Obama: "Neil was among the greatest of American heroes - not just of his time, but of all time. ...
"Today, Neil's spirit of discovery lives on in all the men and women who have devoted their lives to exploring the unknown - including those who are ensuring that we reach higher and go further in space. That legacy will endure - sparked by a man who taught us the enormous power of one small step."
* Edwin "Buzz" Aldrin, who along with Armstrong and Michael Collins formed the crew of the Apollo 11 mission that landed on the moon, in an interview with BBC radio: "We are missing a great spokesman and leader in the space program." Mr Aldrin said he would remember Armstrong "as being a very capable commander and leader of an achievement that will be recognised until man sets foot on the planet Mars".
* Michael Collins: "He was the best and I will miss him terribly."
European Commission President Jose Manuel Barroso:
He was "a source of inspiration for all mankind"
"Neil Armstrong has left an eternal footprint on our memories. His achievements captured our imagination forever and remain a source of inspiration for all mankind."
Jean-Loup Chretien, the first Frenchman in space:
"He was a living legend ... a great man, someone full of self-restraint, extremely discreet."
Jean-Marc Ayrault, France's prime minister: "His famous 'small step' on the lunar surface realised the dream of generations of inventors, scientists, artists, poets or simply amateurs of the beauties of space,"
James Hansen, author of First Man: The Life of Neil A. Armstrong:
"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."
* John Glenn, an original Nasa astronaut who became a US senator from Ohio after his space career, spoke of Armstrong's aversion to the spotlight in a CNN interview: "He was willing to dare greatly for his country and he was proud to do that and yet remained the same humble person he'd always been."
* Charles Bolden, Nasa administrator: "Besides being one of America's greatest explorers, Neil carried himself with a grace and humility that was an example to us all. When President Kennedy challenged the nation to send a human to the moon, Neil Armstrong accepted without reservation.
"As we enter this next era of space exploration, we do so standing on the shoulders of Neil Armstrong. We mourn the passing of a friend, fellow astronaut and true American hero."
* Armstrong family:
"Neil Armstrong was also a reluctant American hero who always believed he was just doing his job. He served his nation proudly, as a navy fighter pilot, test pilot, and astronaut. He also found success back home in his native Ohio in business and academia, and became a community leader in Cincinnati.
"He remained an advocate of aviation and exploration throughout his life and never lost his boyhood wonder of these pursuits.
"While we mourn the loss of a very good man, we also celebrate his remarkable life and hope that it serves as an example to young people around the world to work hard to make their dreams come true, to be willing to explore and push the limits, and to selflessly serve a cause greater than themselves.
"For those who may ask what they can do to honor Neil, we have a simple request. Honor his example of service, accomplishment and modesty, and the next time you walk outside on a clear night and see the moon smiling down at you, think of Neil Armstrong and give him a wink."
* Mitt Romney, US Republican presidential candidate:
"Neil Armstrong today takes his place in the hall of heroes. With courage unmeasured and unbounded love for his country, he walked where man had never walked before. The moon will miss its first son of earth.
"I met and spoke with Neil Armstrong just a few weeks ago -his passion for space, science and discovery, and his devotion to America will inspire me through my lifetime."