In a tweet, King Felipe VI of Spain has said "the world is and will be with France" in the aftermath of tonight's fire.
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What has been destroyed
Here's a look at the section of the cathedral that has been destroyed by the fire.
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Billionaire pledge for cathedral's reconstruction
French billionaire François-Henri Pinault, chairman and CEO of the Kering luxury group, has pledged €100m (£86m; $113m) towards rebuilding Notre-Dame, according to a statement quoted by AFP news agency.
Earlier, President Emmanuel Macron vowed to launch an international fundraising scheme to rebuild the cathedral.
Kering owns the Gucci and Yves Saint Laurent fashion brands.
The treasures of Notre-Dame
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As the wooden rafters burned, the roof, a spire, and much of the cathedral's interior were destroyed.
But some parts of the 850-year-old Gothic building have also been saved.
From rose windows to gargoyles, from bells to relics, we look at what makes the Notre-Dame cathedral so special.
"Notre-Dame is our history, our
literature, part of our psyche, the place of all our great events,
our epidemics, our wars... the epicentre of our
lives.
"Notre-Dame is
burning, and I know the sadness, and this tremor felt by so many fellow French people.
But tonight, I'd like to speak of hope too.
"Let's be proud,
because we built this cathedral more than 800 years ago, we've built it and, throughout
the centuries, let it grow, and improved it.
"So I solemnly say
tonight: we will rebuild
it together."
Images of fire damage
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Flames can be seen from the interior of Notre-Dame cathedral in ParisImage caption: Flames can be seen from the interior of Notre-Dame cathedral in Paris
Images have emerged showing a different view of the damage caused to the cathedral - including a hole reportedly beneath where the spire was positioned.
Getty ImagesCopyright: Getty Images
Smoke rises around the alter in front of the cross inside the building as the fire continues to burnImage caption: Smoke rises around the alter in front of the cross inside the building as the fire continues to burn
Newspaper front pages
The BBC's Neil Henderson has also been sharing some of tomorrow's French and British newspaper front pages on social media - with the Notre-Dame blaze dominating the news agenda.
More from the BBC's Henri Astier, himself a Parisian:
It is impossible to overstate how shocking it is to watch such an enduring embodiment of our country burn.
Locals are not famous for their sunny disposition, but few can walk along the banks of the Seine in the central part of the capital without feeling their spirits rise at the majestic bulk of Notre-Dame.
It is one of the few sights sure to make a Parisian feel good about living there.
Further to its earlier announcement, the office says it is investigating "accidental destruction by fire".
Our history is burning - Macron
Mr Macron also expressed sympathy towards Catholics around the world.
"What's happened this evening is obviously a terrible drama," he said.
"[Emergency services fought the fire] with extreme courage, professionalism and determination... I would like to thank them on behalf of the entire nation.
"This is our history, and it's burning."
'The worst has been avoided'
Speaking at the scene in Paris, President Macron called the fire a "terrible tragedy", but added that the worst had been avoided.
He said he planned to launch a fundraising campaign to renovate the cathedral.
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Getty ImagesCopyright: Getty Images Flames can be seen from the interior of Notre-Dame cathedral in ParisImage caption: Flames can be seen from the interior of Notre-Dame cathedral in Paris 
Getty ImagesCopyright: Getty Images Smoke rises around the alter in front of the cross inside the building as the fire continues to burnImage caption: Smoke rises around the alter in front of the cross inside the building as the fire continues to burn View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter View more on twitterView more on twitter - Read more from our correspondent
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We're now pausing our live coverage, but you can keep up to date with our news stories, video and background briefings on the BBC news website.
Fire 'under control'
The blaze at the cathedral has now been brought under control, says a spokesperson for the firefighters at the scene
'Deeply saddened'
Museums in the Australian state of Victoria tweeted this image of Notre-Dame from a century ago.
Notre-Dame 'will rise from its ashes'
In a tweet, King Felipe VI of Spain has said "the world is and will be with France" in the aftermath of tonight's fire.
What has been destroyed
Here's a look at the section of the cathedral that has been destroyed by the fire.
Billionaire pledge for cathedral's reconstruction
French billionaire François-Henri Pinault, chairman and CEO of the Kering luxury group, has pledged €100m (£86m; $113m) towards rebuilding Notre-Dame, according to a statement quoted by AFP news agency.
Earlier, President Emmanuel Macron vowed to launch an international fundraising scheme to rebuild the cathedral.
Kering owns the Gucci and Yves Saint Laurent fashion brands.
The treasures of Notre-Dame
As the wooden rafters burned, the roof, a spire, and much of the cathedral's interior were destroyed.
But some parts of the 850-year-old Gothic building have also been saved.
From rose windows to gargoyles, from bells to relics, we look at what makes the Notre-Dame cathedral so special.
Australian sorrow
Prime Minister Scott Morrison recalls his visit to the iconic Parisian cathedral
Notre Drame
'Tonight I speak of hope' - Macron
More from the French president:
"Notre-Dame is our history, our literature, part of our psyche, the place of all our great events, our epidemics, our wars... the epicentre of our lives.
"Notre-Dame is burning, and I know the sadness, and this tremor felt by so many fellow French people. But tonight, I'd like to speak of hope too.
"Let's be proud, because we built this cathedral more than 800 years ago, we've built it and, throughout the centuries, let it grow, and improved it.
"So I solemnly say tonight: we will rebuild it together."
Images of fire damage
Images have emerged showing a different view of the damage caused to the cathedral - including a hole reportedly beneath where the spire was positioned.
Newspaper front pages
The BBC's Neil Henderson has also been sharing some of tomorrow's French and British newspaper front pages on social media - with the Notre-Dame blaze dominating the news agenda.
'The heart in ashes'
La Croix, a French Roman Catholic newspaper, has released images of its front page for Tuesday.
France 'touched in its heart'
Former French President Nicolas Sarkozy tweeted to say that France was "touched in its heart, in its identity, in its history".
Former US President Barack Obama tweets
More footage from elevated viewpoint
What Notre-Dame means to the French
More from the BBC's Henri Astier, himself a Parisian:
It is impossible to overstate how shocking it is to watch such an enduring embodiment of our country burn.
Locals are not famous for their sunny disposition, but few can walk along the banks of the Seine in the central part of the capital without feeling their spirits rise at the majestic bulk of Notre-Dame.
It is one of the few sights sure to make a Parisian feel good about living there.
Paris prosecutor opens investigation
Further to its earlier announcement, the office says it is investigating "accidental destruction by fire".
Our history is burning - Macron
Mr Macron also expressed sympathy towards Catholics around the world.
"What's happened this evening is obviously a terrible drama," he said.
"[Emergency services fought the fire] with extreme courage, professionalism and determination... I would like to thank them on behalf of the entire nation.
"This is our history, and it's burning."
'The worst has been avoided'
Speaking at the scene in Paris, President Macron called the fire a "terrible tragedy", but added that the worst had been avoided.
He said he planned to launch a fundraising campaign to renovate the cathedral.
"We will rebuild Notre-Dame."