Northern Ireland's devolved government will get access to an extra £1bn as part of the agreement.

The PM outlines plans designed to address the "anxiety" of EU citizens about their status after Brexit.

The deal will see the DUP support Theresa May in Parliament and £1bn extra cash for Northern Ireland.

Image source, Getty Images

Here's a recap of the day's major events:

• The Conservatives and the DUP have agreed a deal to support Theresa May's minority government, including £1bn extra for Northern Ireland over the next two years

• A three page document, external outlining the terms of the agreement has been published in full
• Downing Street said the money will not be subject to the Barnett formula
• The Labour first minister of Wales condemned the deal as a "straight bung" which "kills the idea of fair funding"

Analysis:

• Laura Kuenssberg: The price of holding power
• Mark Devenport: The deal's impact on power-sharing
• John Campbell: Where is the money going to be spent?
• Brian Taylor: The DUP deal via a Helensburgh swimming pool
• David Cornock: A bung, a bribe or something else?

There was also movement on the UK's plans for EU citizens:

• Theresa May has said she wants EU citizens living in the UK to stay after Brexit as she announced plans designed to put their "anxiety to rest" - but Jeremy Corbyn said the offer was "too little, too late"

• The government also made its 15-page document , externaloutlining the detail of the UK's offer to EU citizens public

You can catch-up with, and watch live, proceedings in Parliament including the statement currently under way in the House of Commons on the Grenfell Tower tragedy with our BBC Parliament colleagues' live coverage.

House of Lords
Parliament

Image source, HoL

Lords leader Baroness Evans tells peers the government has "come out early" with its proposal on EU citizens' rights, which indicates its "seriousness" about finding a solution.

She says the cut-off date will be "a matter for negotiation" and emphasises it is an "early priority for negotiations".

Theresa May has set out the government's "offer" to EU citizens in the UK, telling Parliament that the government wants them to stay.

The prime minister said no EU citizen would have to leave when the UK exits the EU.

The government has proposed giving those with five years' continuous residence, at a cut-off date to be determined by negotiations, a "settled status".

House of Lords
Parliament

The leader of the Lib Dems in the Lords, Lord Newby, says it's to be "regretted" that it has taken so long to set out the government's intentions for EU citizens and "many questions are still unanswered".

He presses for details of a cut-off point after which citizens will not be automatically entitled to apply for residency, and asks about the possibility of ID cards.

House of Commons
Parliament

Plaid Cymru's Liz Saville-Roberts says that whilst the prime minister is bribing the DUP to "stitch up the seams of this threadbare administration", the government continues to neglect the people of Wales and treat them like third class citizens "in this so-called family of equals".

If the government can hand out £1bn to Northern Ireland in a time of austerity, she says, then "where is the £1.7bn that is now so evidently our right?"

Mr Green replies that under the new funding formula, public spending in Wales is now £120 per head for every £100 per head in England.

Liberal Democrat home affairs spokesman Ed Davey has suggested the plans for EU citizens almost amounts to an ID card scheme.

“I have written to the Home Secretary to establish whether this indeed is ID cards by the backdoor and whether EU nationals will now be required to carry them on their person at all times. If so have ministers worked out the practicalities of such a scheme, as well as the cost? The government also needs to explain how an ID card system works when only a small proportion of the population will be required to carry them.”

House of Lords
Parliament

Image source, HoL

Responding to the statement on the proposed deal for EU citizens, Labour's leader in the Lords, Baroness Smith of Basildon tells peers she found David Davis' assurances on how borders would be enforced "unconvincing".

She tells peers other EU leaders "don't share" the prime minister's impression of "a positive response" to her proposals on EU citizens' rights.

She calls it "grossly inefficient and disrespectful" that those who have already applied for residency will now have to apply under the new system.

She refers to a "twilight zone" of uncertainty for EU citizens over their rights to work and travel.

"It has taken a full year for the Prime Minister to come up with a half-baked plan that still leaves in limbo millions of European nationals who have made their home here. This uncertainty is the result of a dysfunctional Government that is not acting in the nation’s best interests.

“The Government should confirm immediately that all EU citizens in the UK by the time we leave can stay indefinitely - this needs to be as simple and comprehensive a process as possible. This will enable UK nationals living in the EU to also have their futures made certain."

House of Commons
Parliament

The DUP's chief whip Sir Jeffrey Donaldson says it is "a remarkable day" when the Labour Party criticise investment in schools, roads, housing, jobs as dangerous to the peace process - adding "it is bonkers to suggest so".

He also adds that Labour frontbenchers should rethink their past comments in support of the IRA and the effect it could have on young people who may be thinking to take up arms in the future.

Mr Green replies that it is clear that anything that aids investment for disadvantaged communities will provide a more positive political atmosphere in Northern Ireland.

House of Commons
Parliament

Labour's Tracy Brabin thanks the Speaker for hosting family day in the House of Commons at the weekend, and points MPs towards the new plaque for her predecessor Jo Cox which was put up in the Commons chamber by her children.

Image source, HoC

Carwyn Jones says the DUP will "screw" the UK government for as much money as they can, and he does not blame them for doing so. The Welsh first minister said it appeared the Prime Minister had discovered a "magic money tree" to provide £1bn just for Northern Ireland, saying it was essentially "cash for votes".

House of Commons
Parliament

The DUP's Westminster Leader Nigel Dodds rises to praise a "good agreement for the UK and a good agreement for all the people of Northern Ireland" - particularly in mental health and hard to reach areas.

He says that his party commits to transparency and that he hopes to one day see published the correspondence from 2010 with the Labour frontbench, and from 2015 with both Labour and the SNP - causing much delight on the Tory benches.

The "faux outrage", he says that has been heard, "is hypocrisy of the highest order".

The DUP looks forward to working with government for the next five years, he says - to deliver Brexit, to strengthen the Union and to deliver security.

Mr Green responds that it has been "a life enhancing experience" and that the government welcome the party's support to strengthen the union and the economy.

Stephen Martin, Director General of the Institute of Directors, said:

“Employers will welcome the constructive clarity of intent offered today and businesses look forward to the UK and EU finally getting down to concrete discussions.

“An aim is obviously not the same thing as a guarantee. Even today, many of the important details are absent, including information on the registration process for EU citizens and when the cut-off date will be. More fundamentally, employers still don’t know what will happen to their EU staff if no deal is reached, questions remain as regards whether or what salary thresholds will apply for workers and their families wanting to remain in the UK. Many EU citizens work part of the year in the UK and part overseas, so will not easily be able to prove their right to remain due to interrupted periods of residence.

“The offer of a two year grace period after we leave for these workers to acquire their right to settled status is welcome, but two years may not be enough and five years would be better. The obligation on individuals who have previously received permanent residency to re-apply must be made as bureaucracy-free as possible, for employers and the individuals concerned alike."

House of Commons
Parliament

Labour MPs Yvette Cooper and Stella Creasy have asked about the situation of women in Northern Ireland who are currently not entitled to free abortions on the NHS in England.

Mr Green has said that this is a devolved matter and therefore an issue for Northern Ireland to decide. Ms Creasy responds that women in Northern Ireland feel as thought they are "forced to pay the price of a forced marriage".

For information on the recent Supreme Court decision on this issue - read here.