US President Barack Obama has called the first man to walk on the moon, Neil Armstrong, a "great American hero" after his death at the age of 82.
Mr Armstrong's family said he died from cardiovascular surgery complications following a heart bypass earlier this month .
The relatives said they were "heartbroken" by his death and called him "a reluctant American hero who always believed he was just doing his job".
They also said they had a simple request to people in memory of his life.
"Honour 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."
Mr Obama, who was seven when the historic mission succeeded, said the astronaut had "delivered a moment of human achievement that will never be forgotten".
As commander of the Apollo 11 mission in July 1969, Mr Armstrong became the first human to set foot on the moon.
Moments after stepping onto the lunar surface, he uttered the famous quote: "That's one small step for man, one giant leap for mankind."
The 38-year-old then spent nearly three hours walking on the moon with Edwin "Buzz" Aldrin.
Mr Aldrin tweeted: "On behalf of the Aldrin family we extend our deepest condolences to Carol & the entire Armstrong family on Neil's passing. He will be missed."
Michael Collins, who also flew to the moon with Mr Armstrong, said: "He was the best, and I will miss him terribly."
Republican presidential candidate Mitt Romney said: "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."
Astronomer Sir Patrick Moore said: "As the first man on the moon, he broke all records. I knew him well. He was a man who had all the courage in the world."
Physicist Professor Brian Cox tweeted: "Sad to hear about death of Neil Armstrong. I do think Apollo was the greatest of human achievements. For once, we reached beyond our grasp."
Former astronaut Tom Jones, who completed four space shuttle flights between 1990 and 2001, told Sky News: "Mr Armstrong was one of the astronauts that was my hero when I was growing up and I watched his initial landing on the moon in 1969 with incredible interest.
"I wanted to do exactly what Neil, and Buzz, and Mike Collins were doing that time. I hoped that one day I would have the chance to participate in the space programme.
"He really was an inspiration to an entire generation of people."
He said meeting Mr Armstrong had been a "dream come true" and described being "star struck" by the chance to meet and work with his idol.
"He's a very unassuming and friendly person when you get to know him in a professional setting," he added.
Jamie Burgess, from the National Space Centre, told Sky News: "It's extremely sad news. It's a terrible shock to the science community. He will be sorely missed."
Hundreds of millions of people watched and listened to the first moon landing - and it was the largest audience for any single event in history.
Mike Cruise, professor of astrophysics and space research at the University of Birmingham, said: "The people at the front of the race always have to tread on new ground.
"He led the whole world into a space era of greater proportion than has been achieved by satellites. You wonder when his first steps will be followed up. It must have been very awe-inspiring to step on to, essentially, a new planet."
Mr Armstrong and his wife Carol married in 1999 and made their home in the Cincinnati suburb of Indian Hill, but he had largely stayed out of public view in recent years.
He spoke at Ohio State University in February at an event honouring fellow astronaut John Glenn and the 50th anniversary of Mr Glenn becoming the first American to orbit the Earth.