Here, we have a look at the issues likely to dominate political discourse in the week to come.
Government formation talks to begin
Fianna Fáil and Fine Gael are to begin government formation talks tomorrow, after a meeting between Taoiseach Simon Harris and Tánaiste Micheál Martin on Monday.
A joint statement said Micheál Martin and Simon Harris had a "positive and constructive" engagement.
“The two party leaders met today and had a positive, constructive engagement,” the statement said.
“The Taoiseach and Tanaiste agreed the need for a stable government, underpinned by mutual respect and clear policy direction, for the next five years, so that it can deliver for the Irish people in the face of great challenges.
“The two party leaders have now asked their negotiating teams to commence talks tomorrow.”
The negotiating teams for both parties will meet tomorrow to discuss policy.
Both leaders had phone calls with Labour Party leader Ivana Bacik today, while Simon Harris has started meeting a swathe of Independents on an individual basis.
Despite an apparent ramping up of discussions, it's still unlikely a government will be in place for the return of the Dáil on December 18th.
Early to mid-January is believed to be the most likely time for a full agreement on the shape of the next government.
Sources have indicated that Mr Martin and Mr Harris favour a deal with Independent TDs rather than Labour or the Social Democrats.
Together, Fianna Fáil and Fine Gael have 86 seats, two short of a Dáil majority. However, they will likely target around 90 seats for a strong majority.
Fianna Fáil has the stronger negotiating position, as they have 48 seats to Fine Gael's 38.
Reports have indicated Fianna Fáil will push for a longer spell for Mr Martin as leader in any rotating taoiseach arrangement, possibly three years to two.
Other issues will include how important ministeries are divided, and how many Cabinet seats each party gets.
'Parity' is the buzzword
Fine Gael has indicated they will seek "parity", mentioning the word in a number of press statements.
Speaking at the weekend, the Taoiseach said it should not be taken for granted that his party will be in the next government.
"There is far too much presumption in relation to the outcome of government talks before government talks have even taken place," Mr Harris said.
"I wouldn’t take my party for granted and I think fewer public musings and more concrete engagement is the way to proceed."
Mr Harris may well have to concede on the issue of a shorter spell as taoiseach.
The division of Cabinet roles is likely to be a more difficult point in the negotiations.
Junior ministerial roles could be important to keep figures across the parties happy.
This could be more difficult if the former, and soon to be current, coalition partners go for the Labour Party or Social Democrats to form a government.
That brings us to the next point...
Labour, Social Democrats, or Independents?
Social Democrats leader Holly Cairns has said her party will play an "important role" in the 34th Dáil, but it looks increasingly likely that will be from the opposition benches.
Labour Party leader Ivana Bacik seems more unsure, and there is understood to be varying views within her party on whether going into power or opposition is the best route.
Ms Bacik is set to meet with Mr Harris and Mr Martin for talks this week.
In reality though, it looks like Fianna Fáil and Fine Gael will look to Independents for a steady majority.
What parties would you like to form the next government?
- Fianna Fáil, Fine Gael and Independents
- Fianna Fáil, Sinn Féin and Independents
- Fianna Fáil, Fine Gael and the Labour Party
- Fianna Fáil, Fine Gael and the Social Democrats
- Other combination (let us know in the comments).
Mary Lou McDonald's appeal to Fianna Fáil rings hollow
Sinn Féin leader Mary Lou McDonald has criticised Fianna Fáil for their refusal to talk, but this stance is hardly new.
She accused Mr Martin of "looking down his nose" at people who voted for Sinn Féin.
"They're [Fianna Fáil] talking to Independents, they've talked to others. Interestingly, the only group that they've steadfastly refused to speak to is the second largest party in the Dáil, and I really think for Micheál Martin to look down his nose at over 400,000 people who voted for Sinn Féin and to disregard those votes en masse is really a bad look."
The comments seem more performative than anything though, as Ms McDonald and her colleagues would likely prefer another few years in opposition rather than governing with a party they have consistenly said needs to be removed to "change the government".
Abroad
The fall of Syrian president Bashar Assad’s government continues to reverberate around the world, with Russia president Vladimir Putin providing asylum for Assad.
In the UK, Labour prime minister Sir Keir Starmer has said his government is not planning any more tax cuts, but that they cannot be ruled out.
In the US, fears are mounting over president-elect Donald Trump's pledge to deport millions of migrants and to pardon many of those who are currently serving prison sentences for their role in the US Capitol riot.
