Shortly before 11.00am UK time (5.58 E.T), the crew was due to open the hatch of their Dragon spacecraft and enter the deadly vacuum of space.
Billionaire Jared Isaacman and SpaceX employee Sarah Gillis will then take turns exiting the vehicle, 435 miles (700km) above Earth.
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Watch Dragon’s first spacewalk with Polaris Dawn crew
Cabin being vented
The pre-breathing process has now finished and the crew has started venting the cabin.
Spacce X has said the pressure inside the cabin has started to go down.
WATCH: Astronauts prepare for spacewalk
What is the pre-breathe process?
Astronauts must complete the pre-breathe phase before they are able to exit the capsule.
The process takes around 19 minutes and involves astronauts breathing in oxygen to purge the body of nitrogen.
Divers use a similar procedure.
Pictured: Isaacman waiting to open the hatch
The astronauts are still in the ‘pre-breathe’ phase and are waiting to be given the clear to open the hatch.
Spacewalk now underway
The pressurisation of the space suits has started – a process which is due to take around three and a half minutes.
This means the spacewalk has officially begun!
The astronauts have been given the go ahead to complete the mission.
WATCH: SpaceX Polaris Dawn spacewalk – Billionaire attempts to make history
Initial safety checks completed
The audio from Space X’s live broadcast indicated that the initial safety checks on the spacesuits have been carried out.
The final checks on the safety equipment are currently underway.
First images from inside Dragon capsule
The faces of Jared Isaacman and Scott Poteet have been seen for the first time today inside the capsule.
Spacewalk due to begin shortly
The final checks are now being carried out and the mission is due to begin within minutes.
The first live footage has also been shown from inside the Dragon capsule on the SpaceX broadcast.
How far above Earth are the astronauts?
What suits will the crew be wearing?
Astronauts put on space suits and start ‘pre-breathing’
The astronauts have already put on their space suits and have started ‘pre-breathing’ .
A host on the SpaceX live broadcast said: ‘They’ve been undergoing a process called pre-breathing, where the atmosphere pressure inside Dragon is slowly decreased and oxygen is increased, to prepare their bodies for the [spacewalk] suit environment.’
He added that they began putting on their space suits ‘some time ago’.
Exclusive:The potentially deadly risks of the spacewalk
Spaceflight safety experts have warned the crew faces potentially deadly risks of radiation exposure and rapid changes in pressure that can cause life-threatening sickness.
Who is billionaire Jared Isaacman?
The billionaire Jared Isaacman, 41, is most well known as the founder and CEO of the American payment processing company Shift4.
Isaacman founded the company in 1999 out of his parent’s basement when he was just 16 years old.
After dropping out of high school to work as a cybersecurity consultant, Isaacman used a $10,000 loan from his grandad to convince a bank to certify him to sell credit card terminals.
That business ballooned and now handles transactions for a third of America’s restaurants and hotels – processing more than $200 billion in payments every year.
Why is the mission so dangerous?
Previously only state-backed space agencies have sent astronauts on spacewalks due to the extremely high risks involved.
Floating beyond the protective walls of a spacecraft is considered to be one of the most dangerous tasks an astronaut can undertake.
In this case, that risk will only be heightened by the fact that none of the crew except for Isaacman have ever been in space before.
Additionally, since the Dragon spacecraft does not have an airlock, the entire craft will need to be depressurized at once.
That will expose all four crew members to the harsh conditions of low orbit and will break the current record for most people simultaneously in the vacuum of space.
What has happened on the mission so far?
The Polaris Dawn mission launched from the Kennedy Space Centre in Florida on September 10 at 5:23 am ET after days of delay due to weather and a helium leak.
Yesterday, the SpaceX Dragon Crew spacecraft carried its crew to an altitude of 870 miles (1,400 km) above Earth – the highest any human has been since NASA’s Apollo missions.
The crew have already made a pass through Earth’s Van Allen Belt – a region of extremely high radiation.
However, the mission’s most dangerous moment will come today as the crew embark on the first private spacewalk.
‘Strive to greater heights’ – Elon Musk
A minute-by-minute breakdown of the mission
10.58am UK time: The mission begins
11.28am:Â Hatch will be unlocked and opened
11.31am:Â Mission commander Jared Isaacman will exit and begin suit tests
11.44am:Â Isaacman goes back to his seat
11.49am: Mission specialist Sarah Gillis exits
11.57am:Â Gillis returns to her seat
11.58am: Hatch is shut and repressurisation begins
12.48pm: Repressurisation finishes
Who are the Polaris Dawn crew?
Onboard are the billionaire Jared Isaacman, former airforce commander Scott ‘Kidd’ Poteet, and SpaceX employees Sarah Gillis and Anna Menon.
Apart from Isaacman, none of the all-civilian crew attempting this dangerous mission have any experience in space.
Welcome to MailOnline’s coverage of the SpaceX Polaris Dawn spacewalk
The first ever privately funded spacewalk is due to start just before 11am (5.58 E.T.) UK time.
It had been due to start at 7am but this was pushed back without any reason given for the delay.
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SpaceX Polaris Dawn LIVE: Billionaire Jared Isaacman and astronaut crew embark on ‘dangerous’ world first private spacewalk