SpaceShipOne has rocketed into the history books to become the first private manned spacecraft to fly to the edge of space and back.
SpaceShipOne lands after its 90-minute flight
The craft, built by aviation pioneer Burt Rutan, went over space's 100km (62 mile) boundary, said mission control.
It was carried to 46,000ft (13.8km) by its launcher White Knight at which point it was unleashed. It fired its rocket to continue its trip.
Mr Rutan was on the runway to embrace pilot Mike Melvill on his return.
They paid an emotional tribute to each other after the flight.
"It was a mind-blowing experience, it really was. Absolutely an awesome thing," said Mr Melvill.
"Burt thought of everything to make it work and it all worked exactly as he told us," he added.
Mr Melvill said the view from space was "spectacular", and he was only sad that Mr Rutan, who he described as his "best friend in the whole world", could not have been there, too.
A delighted Mr Rutan said it had been an emotional journey.
"The way you guys felt when you saw it touch down, we felt that several times in mission control during the flight," he said.
Cheers and applause
Applause and cheering broke out when the first confirmation of its altitude was announced.
"Beautiful sight, Mike," mission control said to pilot Mr Melvill as the gliding spaceship made its way to touch down at California's Mojave Airport.
It finally came back to Earth at 0815 PDT, after its 90-minute flight.
Messages of congratulations came from Nasa's administrator Sean O'Keefe, who called it a "remarkable achievement".
Steve Bennett, chief of the British civilian space project, Starchaser Industries, said it was a "marvellous achievement", but that he was slightly envious.
"This just proves that you don't have to be Nasa or a government organisation," he said.
His team plans to launch its own rocket in about 18 months.
About 3,000 people, including over 500 media crews, descended on the desert to watch the historic flight.
The pilot, 62-year-old Scaled Composites vice-president Mr Melvill, stamped his name in the record books as the first non-government-funded pilot to fly a spaceship out of Earth's atmosphere.
After Monday's flight he told the crowd: "I think I'll back off a little bit now and ride my bike."
Mr Melvill said he had heard a loud bang during the record-breaking mission.
On the ground, he pointed out a section at the back of the craft where a part covering the nozzle had buckled, suggesting it may have caused the odd noise.
Mr Rutan confirmed in a press conference that it was not a "perfect flight", and that his team would be assessing data and addressing some "anomalies" that had occurred.
Mr Rutan characterized them as the most serious the team had encountered since the test flights of SpaceShipOne began, and put SpaceShipOne 35km (22 miles) off target for re-entry.
Next stop X-prize
SpaceShipOne glided very briefly after its launch from White Knight before firing up its rocket for about 80 seconds.
It then blasted off to reach its target height in a vertical climb at more than three times the speed of sound.
The vehicle then altered its wing configuration to allow for high drag, and fell back towards Earth during which the pilot was weightless.
At this point, Mr Melvill admitted he opened up a packet of chocolates to see them float.
At re-entry, the ship's wings were again reconfigured to allow the craft to glide back down to Mojave Airport in about 20 minutes.
Mr Rutan said that, in the next few days, the team would make a decision about its attempt to claim the Ansari X-prize.
He will then inform the X-Prize Foundation, effectively giving it, and the world, 60-days' notice of SpaceShipOne's attempt.
The $10m (£5.7m) prize will be awarded to the first non-government, manned flight into space.
To beat 25 other teams in this race, SpaceShipOne must reach 100km twice in two weeks.
On each occasion it will have to fly with a pilot and at least the ballast equivalent of two other people.
Mr Rutan told the press conference that the team would "probably" attempt the two flights within one week.
When the X-Prize is won, it could open up the skies to future tourist trips to the edge of space for those looking for something a bit different in their lives.
The craft escaped Earth's atmosphere on Monday, but was unable to orbit the planet because of the speed it was going.
Going sub-orbital is cheaper and far less risky, but it still means the pilot - or any passenger - has a stunning view of Earth.
Burt Rutan has been widely acclaimed for his pioneering achievements in the field of aviation.
SpaceShipOne was carried by White Knight
White Knight and SpaceShipOne are thought to be revolutionary in many ways. SpaceShipOne and White Knight can be reused.
SpaceShipOne's rocket motor, which was custom-built by SpaceDev of San Diego, burns a solid rubber propellant with liquid nitrous oxide - a liquid version of "laughing gas".
It is more environmentally friendly than some other space rocket fuels.