Jayne McCormack
BBC News NI political correspondent

We now interrupt these proceedings... if you're wondering what just happened, so are we.

The DUP chose Paul Givan to be education minister, but Sinn Féin then asked for a break in the process as they said it ran contrary to their understanding.

The talk here a short time ago was that Sinn Féin would pick education, we aren't clear what was agreed or how this is going to go, but could this be, already, the first row?

Paul Givan of the DUP has been appointed education minister.

He is a former first minister.

Image source, PA Media

Sinn Féin assembly member Conor Murphy is appointed minister for the economy.

He's a veteran republican politician and has previously held the role of finance minister in the Stormont executive.

Image source, PA Media

Alliance leader Naomi Long is appointed justice minister.

This appointment of this role sits outside the D'hondt process and is decided by a cross-community vote.

Long served as justice minister during the previous assembly before it's collapse.

Image source, PA Media

Michelle O'Neill and Emma Little-Pengelly speaking for the first time as first and deputy first minister.

Image source, PA Media

Ireland's Tánaiste (deputy prime minister) and minister for foreign affairs Micheál Martin says it is a "special day for the people of Northern Ireland".

He congratulates Michelle O’Neill and Emma Little-Pengelly on assuming their roles as first minister and deputy first minister.

He says that the Irish government "stands ready to support the work of the Executive and to work in partnership with the British Government".

Mr Martin adds that he looks forward to a meeting of the North-South Ministerial Council.

The five-minute warning bell has rung alerting assembly members to return to the chamber.

Northern Ireland is divided into 18 constituencies. Each constituency elects five MLAs, making a total of 90 MLAs.

Sinn Féin is the largest party with 27 seats, the Democratic Unionist Party (DUP) is the second largest with 25 seats.

The Alliance Party has 17 seats.

The Ulster Unionist Party (UUP) have 9 seats and the Social Democratic Party and Labour Party (SDLP) have 7 seats.

Sinn Féin, DUP, Alliance and UUP will all have ministers in the executive but the SDLP don’t qualify for a position as they don’t have enough seats.

These numbers will be important once D'Hondt starts running and ministers are appointed.

Government departments in Northern Ireland are allocated using the obscure-sounding D'Hondt mechanism, but what does this entail?

Stick with us as we explain.

There are nine departments in the Northern Ireland Executive, which operates as a coalition.

These need to be shared out among the parties who gained the most seats in the assembly election and the D'Hondt mechanism is used to calculate who gets what.

But one department - justice - is decided differently. More on that later.

The Good Friday Agreement stipulated that the D'Hondt system should be used to share out Stormont ministries between the parties, as it was felt to be suitable for use in a divided society, aimed at ensuring cross-community representation.

It uses a mathematical formula which involves the principle of "highest average".

This means it tends to favour larger parties: the idea is that it reflects the strength of a party's total support by taking into account the number of seats it won in the election.

Departments are assigned one at a time, beginning with the party with the highest total.

As the largest party, Sinn Féin has the first choice of ministry, followed by the DUP, the second largest party, and so on.

The system differs from the single transferable vote (STV) in that it does not use a quota or formula to allocate seats or posts.

Ross McCrea
Live page reporter

Image source, PA Media

A number of prominent Sinn Féin figures were in the public gallery to watch Michelle O'Neill take on the role of first minister.

They included Sinn Féin Finance Spokesperson Pearse Doherty, party leader Mary Lou McDonald, former MEP Martina Anderson, former president of Sinn Féin Gerry Adams and Fiachra McGuinness, son of the late Martin McGuinness.

Northern Ireland Secretary of State Chris Heaton-Harris welcomes the return of power-sharing at Stormont.

He says it is a "great day" for Northern Ireland and its people and believes the newly established executive will be "sustainable".

Image source, PA Media

The NI Secretary says that now that Stormont is back the £3.3bn funding package is now "free to flow".

He says the return of a functioning power-sharing executive will now see the UK Treasury release a financial package earmarked to help struggling public services in Northern Ireland.

Three deputy speakers have also been elected to the assembly, they are Caral Ní Chuilin of Sinn Féin, John Blair of Alliance and Steve Aiken of the Ulster Unionist Party.

DUP MP Gregory Campbell, a former minister in the Northern Ireland Executive, says today's return to Stormont is ‘a significant day’.

He says the DUP achieved ‘seismic change' and that is why the party has returned to Stormont.

On the subject of Michelle O’Neill appointed first nationalist first minister, he told BBC News NI political editor Enda McClafferty that his thoughts are with people who lost loved ones in the past, and that he hopes Ms O’Neill’s appointment ‘puts that back into the distant past’ for many people watching on.

He defended the appointment of his DUP colleague Emma Little-Pengelly as deputy first minister without having been elected, saying voters will soon have the opportunity to cast their votes in upcoming elections.

Don't worry, it's just for 30 minutes, hopefully not two years.

We've still lots to update you on in the meantime.

Following the appointment of the first minister and deputy first minister, the speaker has announced a short break after which other ministerial roles will be filled.

Image source, PA Media

SDLP MLA Justin McNulty remains in the chamber despite another obligation calling.

The representative for Newry and Armagh is also an inter-county GAA manager, after taking the reins of Laois senior football team late last year.

The team is due to face Wexford in Division 4 of the Allianz Football League at 1800

The venue is Chadwick’s Wexford Park in Wexford, a more than three-hour drive from Stormont.

Independent assembly member Claire Sugden congratulates Michelle O'Neill and Emma Little-Pengelly in their new roles.

She says they are both "capable, strong women" who have "worked in politics for a long time and will work despite the misogyny".

SDLP assembly member Matthew O'Toole, speaks for the first time as leader of the opposition.

Amid the symbolism of the day, O'Toole cautions "symbolism will not pay teachers and nurses".

He adds: "Selfies won't cut waiting lists."

The focus of the executive now needs to be on improving public services, according to O'Toole.

After inviting both the first and deputy first ministers to commit to never collapsing the institutions again, he said the opposition would provide "long awaited accountability".

TUV leader Jim Allister says the DUP's deal is the "consummation of enthroning a Sinn Féin first minister with the unelected bridesmaid as deputy".

He adds: "We have a Sinn Féin first minister, but not in my name nor in the name of thousands of other unionists."

Enda McClafferty
BBC News NI political editor

Image source, Stormont

After almost two years Michelle O’Neill’s moment has finally arrived.

She is no longer first minister in waiting and can now take her place in history as the first nationalist to hold that office.

In a place where symbolism matters, it is a significant day in Northern Ireland’s 103-year life span.

But with the new office comes new pressure as Michelle O’Neill has pledged to be a first minister for all.

To fulfil that promise she will have to move well beyond her comfort zone.

She has had two years to prepare, so we can expect a number of firsts in her new role have already been earmarked.

Rising to the office may be the easy part, but rising to the task could be a much greater challenge.

Alliance leader Naomi Long extends her congratulations to the new speaker and first and deputy first ministers.

"It is a huge burden to lead the executive, particularly in the challenging times we find ourselves in," she adds.

"I have no doubt whatsoever you will be up to the task."