The EU's chief Brexit negotiator Michel Barnier has been showing the world, via Twitter, what the EU's negotiating team looks like.

He also said he had read the UK's letter and told reporters at a summit in Malta that "we're ready". Other than that, he made no further comment. 

BBC Newsnight

Columnist Tim Montgomerie argues politicians should focus on our post-Brexit future.

As Theresa May triggers Article 50 to formally trigger the Brexit process, former UKIP leader Nigel Farage says he's thrilled to have made it to this point.

As Article 50 is triggered, here's what some people will miss about EU membership, and what some won't.

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Although the UK's letter does not repeat the PM claim's earlier this year that "no deal is better than a bad deal", she does say that security co-operation would be "weakened" in the event that an agreement might not be reached.

This is the key passage from the letter on this. 

Image source, AP

The pound has strengthened slightly against the euro after the long-awaited triggering of Article 50 although market reaction was fairly muted. 

The pound rose by 0.6% against the euro by the time the prime minister had finished her address to Parliament. 

However, the UK currency showed little movement against the US dollar in the immediate aftermath, remaining marginally lower at 1.245 US dollars.

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Parliament

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Conservative Anna Soubry suggests that in the next two years the EU may abandon the principle of freedom of movement.

If this happens will the prime minister reconsider her decision to leave the single market? she asks. 

She suggests this would help businesses, ease the political situation in Northern Ireland and would "see off the SNP's oturageous demand for a second referendum".

What matters, replies Theresa May, is not the structures but the outcome - "free and frictionless access to the single market".

House of Commons
Parliament

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Angus Robertson says that in Scotland, 62% to remain in the European Union. Every single local government area in the country voted remain.

Last year, Mr Robertson says he raised the PM's commitment to a UK-wide approach, and since then the Scottish government has published a compromise plan.

The PM could have taken the views of the Scottish, Welsh and Northern Ireland governments seriously - but she did not, Mr Robertson says.

And he goes on to say the UK is not a united kingdom; and if she continues to ignore Scottish views, she "will make Scottish independence inevitable".

Theresa May says that the SNP want Scotland to be treated differently because they voted to remain.

"My own constituency voted to stay in the EU," she says adding that the referendum "was a vote of the whole of the UK".

Theresa May's letter to European Council president Donald Tusk sets out the UK's intent to withdraw.

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UKIP leader Paul Nuttall says he is happy about the stage that has been reached but suggested the job of extricating the UK from the EU was far from done.

The BBC's Laura Kuenssberg tells the BBC's Daily Politics that the tone of letter is very different from the PM's previous major speeches on Brexit. 

She says the government has been very keen to distance itself from talk of transitional agreements or a phased withdrawal but it is now clear that the UK is seeking a "soft departure" from the EU in some areas.

She adds that it is clear that some powers will be returned to the Scottish government and other devolved administrations after the UK leaves.

House of Commons
Parliament

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The Lib Dems will not roll over as the official opposition has done, says Lib Dem Leader Tim Farron.

He tells MPs that he will able to look his children and grandchildren in the eyes and say he did everything he could "to prevent this calamity".

He asks who should sign off a final Brexit deal - should it be the politicians or the people?

Theresa May says it was the Lib Dems who wanted a referendum on the EU in the first place.

"We gave it to them and now we are abiding by it." 

The BBC's Alex Forsyth has been combing the Article 50 letter and here are some of the key points she has drawn out.

• The PM acknowledges UK will lose influence over the rules and there will be consequences. She says she knows UK companies will have to abide by rules of institutions of which they are no longer a part.
• Theresa May uses risk of support for security & anti-terror measures being weakened to argue against no deal being reached.
• She asks for early agreement on the principle of phased implementation – ie a transitional agreement on the terms of exit. 
• The letter repeats several times the UK’s view that they have to discuss a future deal as well as withdrawal at the same time, not one after the other.

SNP Westminster leader Angus Robertson claims Scottish independence will be "inevitable" if Theresa May "does not respect the differences" across the nations of the UK about Brexit.

Arguing that Scotland voted to remain in the EU, he accuses Mrs May of breaking her word by not coming to an agreement before triggering Article 50.

He told the PM: "You said you think Brexit will bring unity to the United Kingdom. It will not. On this issue it is not 'a United Kingdom' and you need to respect the differences across the nations of the UK.

"If you remain intransigent, you will make Scottish independence inevitable."

Mrs May replied that the EU referendum had been a vote "of the whole of the United Kingdom", and she added: "You forget that something like 400,000 SNP supporters voted to leave the EU."

The Daily Politics

Andrew Neil on the Daily Politics says there is not much new in the Article 50 letter but one key point is that the UK has made clear it wants talks on the divorce agreement and a future relationship to be conducted simultaneously. 

This is important because some people in Brussels want the two strands to be separated from each other, which critics say makes an overarching deal less likely.