In quotes: Reaction to Article 50 being triggered
Prime Minister Theresa May said: "This is an historic moment from which there can be no turning back - Britain is leaving the European Union - we're going to make our own decisions and our own laws, we're going to take control of the things that matter most to us.
"And we're going to take this opportunity to build a stronger and fairer Britain that our children and grandchildren are proud to call home."
Labour leader Jeremy Corbyn said his party respected the decision of the British people to leave the EU.
"Today we embark on the country's most important negotiations in modern times.
"The next steps along this journey are the most crucial, and if the prime minister is to unite this country, as she says she aims to do, the government needs to listen, consult and represent the whole country, not just the hard-line Tory ideologues on her own benches."
I'll go for a pint of something and think to myself that, after 25 years of slog, perhaps it was all worth it"
German Chancellor Angela Merkel said: "We Germany, but also Britain's other partners in the EU, certainly didn't want this day to come because we're losing a strong and important member state. But naturally we accept the democratic decision of the British voters, and with the triggering of Article 50 we now have greater clarity about how the British side envisages the way ahead and which goals Britain wants to pursue in the negotiations."
European Parliament Brexit negotiator Guy Verhofstadt said the rights of UK citizens living in Europe and EU citizens in Britain were paramount.
"We don't think that citizens should become bargaining chips in a negotiation," he said, adding that there could never be a situation where it is better to be outside the EU than inside and that is "not about revenge or punishment".
Scottish First Minister Nicola Sturgeon tweeted: "Today, the PM will take the UK over a cliff with no idea of the landing place. Scotland didn't vote for it and our voice has been ignored."
Lib Dem leader Tim Farron said: "I believe the prime minister is twisting the will of the people, leaping into the abyss without any idea of where our country will end up.
"Theresa May has chosen the hardest and most divisive form of Brexit, choosing to take us out of the single market before she has even tried to negotiate."
European Council President Donald Tusk said invoking Article 50 was not a happy occasion. "There is nothing to win in this process - and I am talking about both sides. In essence, this is about damage control.
"We already miss you. Thank you and goodbye."
Former UKIP leader Nigel Farage said he felt "thrilled because I know that at 12:30 today we passed the point of no return".
He added: "There will be lots of arguments and debates over the next few years - but we're leaving, so I couldn't be happier really.
"I'll go for a pint of something and think to myself that, after 25 years of slog, perhaps it was all worth it."
There seems to be very little understanding of the reality of what's going to face us in these negotiations"
Former Labour leader Ed Miliband urged Mrs May to work hard to recapture the national unity "which, frankly, eludes us at the moment".
"The eventual deal we get must work for the 48% as well as the 52% because, whether we were Remainers or Leavers, we'll all live in the same country together after Brexit.
"But can I emphasise to her that national unity must be earned and not just asserted, and it must be shown in deeds and not just in words? And we are a long, long way from it, and I hope that she'll agree with that."
SNP Westminster leader Angus Robertson said: "She said she thinks Brexit will bring unity to the United Kingdom. It will not. On this issue it is not 'a United Kingdom', and she needs to respect the differences across the nations of the UK. If she remains intransigent, she will make Scottish independence inevitable."
Stephen Martin, the Institute of Directors director general, urged ministers to go for a smooth Brexit, with new trading arrangements agreed "before we walk through the exit door".
"Success means listening to business on the vital priorities of maintaining tariff-free trade, minimising customs red-tape and keeping the bureaucratic hurdles to bringing in necessary skills as low as possible."
Paul Drechsler, CBI president, said: "It is in the interests of businesses across Europe to work together in absolute determination to make a success of Brexit.
"Our shared aim must be to forge a mutually beneficial deal that delivers barrier-free trade and safeguards prosperity for all. The prime minister has recognised this."
Former Conservative minister Alistair Burt said: "Like millions of others in the United Kingdom, I'm proud of the European Union and the contribution the United Kingdom has made to the European Union during my political lifetime, and I am a little sad today. But I do stand unequivocally with the prime minister as she calls for a united approach to a new future."
European chief negotiator for Brexit Michel Barnier told the BBC he had read Theresa May's letter to the EU, triggering Article 50, adding: "We're ready."
TUC general secretary Frances O'Grady urged the prime minister to take her time "to get the best deal for Britain - not just the fastest deal", adding: "British workers and British jobs are relying on it.
"The best deal will guarantee that hardworking Brits keep their hard-won rights at work - and that in the years to come they won't miss out on new protections that Dutch, Spanish and German workers get."
Former Labour shadow home secretary Yvette Cooper said the prime minister must not "unintentionally lead the break-up of Britain" through her pursuit of Brexit.
"But she will also know that holding us together requires more than just the rhetoric of unity, so can she say what she will do in both the content and style of your negotiations?
"Not to fuel further division, not to play into the hands of others but to ensure that voices from all over the country are genuinely heard in this debate, so that she does not become the prime minister who unintentionally leads the break-up of Britain."
Gina Miller, the businesswoman who brought the landmark legal challenge to get Parliament to vote on whether the UK could begin the process of leaving the EU, said she was "filled with trepidation and anxiety" following the triggering of Article 50.
"There seems to be very little understanding of the reality of what's going to face us in these negotiations.
"It seems to be 'Mrs May's way or no way' - that closed stance is not best for the whole of Britain".
Former Conservative minister Claire Perry praised Mrs May's "clear, concise and very generous" approach to the Brexit talks, but urged her to reject the idea that no deal would be OK.
"As we go into a period of really enhanced risk and uncertainty for our country and for businesses... does she not agree with me it's time to start talking facts and sense to the British people rather than rhetoric and ideology?
"In particular, rejecting the idea that no deal and a reliance on WTO [World Trade Organisation] rules would somehow be OK."
Plaid Cymru Westminster leader Hywel Williams told Mrs May: "There must be a better way than just her way."
"Fairness is just that, the proper respect for all views from all parts of the island, not just, as she puts it, taking into account specific interests of nations and regions beforehand, not just consulting on which repatriated powers should stay in Westminster and which should be dribbled down, whilst she drives through her extreme version of Brexit."
DUP deputy leader Nigel Dodds said his party believed Mrs May to be the right leader to steer the country through the Brexit challenges ahead.
"The prime minister has rightly been emphasising her determination to deliver for all constituent parts of the United Kingdom on this historic day.
"And whilst others are content to moan and whine, we want to see that delivery happen and we are confident she will make that happen."
Former Conservative minister Anna Soubry urged the prime minister to reconsider staying in the single market if the EU abandoned its commitment to the free movement of people.
"It's what British business wants, it would see off Nicola Sturgeon and the SNP's outrageous demands for a second referendum, and these are serious matters that this United Kingdom faces."
Miles Celic, chief executive of TheCityUK, called for continued access to high quality talent from Europe and beyond.
"For the UK-based financial and related professional services industry, the right Brexit deal will be bespoke, underpinned by mutual market access and based on mutual recognition and regulatory cooperation."
Antonio Tajani, President of the European Parliament, said: "Today isn't a good day. Brexit marks a new chapter in our union's history, but we're ready, we'll move on, hoping the UK remains a close partner."
Former Conservative Deputy Speaker Nigel Evans said: "Well this is truly a red, white and blue letter day, and it represents all of the constituent parts of the United Kingdom, including Scotland. Sending it ambassador class was a nice touch, prime minister."
The SNP's Owen Thompson said: "The prime minister told us Brexit meant Brexit.
"But now when we see the Scottish parliament voting for a second Scottish referendum, would the prime minister realise and acknowledge that Scotref means Scotref, and agree to any application for a Section 30 [the order allowing a second Scottish independence vote]?"
Conservative MP Jacob Rees-Mogg, a prominent Leave campaigner, quoted Sir Francis Drake and "Gloriana", a moniker for Queen Elizabeth I, as he welcomed the news.
"Does she recall the words of Francis Drake? There must be a beginning of any great matter, but the continuing unto the end until it be thoroughly finished yields the true glory. May I wish her good luck and good fortune in her negotiations, until she comes to true glory and is welcomed back to this House as a 21st century Gloriana."
Conservative MP Peter Bone said: "Some members on both sides of this House have been working all their political career to extract the United Kingdom from the European super state.
"Sometimes we were isolated, sometimes we were ignored, and sometimes we were insulted. But thanks to the British people, today we're leaving the European Union."
Adam Marshall, director general of the British Chambers of Commerce, called for "a pragmatic and grown-up dialogue on the real-world issues, rather than verbal volleys between London and Brussels" to maintain business confidence over an uncertain two years.
EEF chief executive Terry Scuoler said securing a deal within two years would be "fiendishly difficult if not impossible", and said Mrs May must be ready to seek a transition period to settle new arrangements rather than adopting "cavalier or ill-judged negotiating positions" which could end in her walking out without a deal.
"A deal that leads to more bureaucracy and more cost for companies would be a very poor deal for Britain. Both sides should work towards a form of regulatory co-operation that allows current comprehensive trade arrangements to continue and make little or no change in the regulatory environment before a negotiated deal has time to bed in."
Airport Operators Association chief executive Karen Dee said the organisation shared the government's confidence that new agreements on air traffic rights with the EU and countries like the US and Canada can be secured.
But she warned: "The alternative, the disappearance of the legal framework for around 85% of the UK's air traffic with no World Trade Organisation-style fall-back option, would be very disruptive for both sides."
Former SNP leader Alex Salmond questioned whether now was the right time for the prime minister to trigger Article 50, claiming her approach over the last nine months had left Northern Ireland "deadlocked", Wales "alienated" and Scotland "going for a referendum", while the English are "split down the middle" over Brexit.
Former Labour minister Baroness Smith of Basildon said the Article 50 process "must not be so ideologically driven that the government accepts anything and claims it's a good deal". She also criticised the unintentional connection between trade and national security in the letter to Mr Tusk, saying "it appears to state if we can't reach an agreement on trade, this will have an impact on security".
Mike Cherry, national chairman at the Federation of Small Businesses, said: "FSB members want to see the easiest possible access to the single market.
"There must also be reassurance for small businesses which employ non-UK EU citizens, and rely on the ability to recruit those with the skills and talents they need."