Here, we have a look at the issues likely to dominate political discourse in the week ahead.
Row over Regional Independents speaking time
Controversy has erupted after Ceann Comhairle Verona Murphy ruled that Regional Independent TDs who support the government, but are not ministers, will be granted opposition speaking time.
She said a precedent for this was set during the confidence and supply agreement between Fianna Fáil and Fine Gael in 2016, during which Fianna Fáil "was still considered the main opposition party".
She has invited any members of the Dáil Business Committee who do not agree to make a submission outlining any alternatives by close of business next Wednesday.
A recognised group has more speaking rights within the Dáil than an unaffiliated backbencher, such as the entitlement to ask questions to the Taoiseach during Leaders’ Questions.
The Regional Independents grouping of TDs and Independent Kerry TDs and brothers Michael and Danny Healy-Rae have agreed to support Fianna Fáil and Fine Gael in the new government, which is set to be formally appointed on Wednesday.
The decision has been heavily criticised by opposition parties.
Labour TD Duncan Smith called it unacceptable.
"It is the responsibility of all in politics to improve politics reputation and standing in public life," he said
"The people would feel like a stroke is being pulled and would cause huge reputational damage to this Dáil."
Sinn Féin has said it will seek legal advice over the decision.
A Sinn Féin spokesperson told RTÉ the party "is deeply concerned that this proposal, where TDs who support the government and who helped draft the Programme for Government, would sit on the opposition benches to avail of extra speaking time intended for the opposition".
They added: "Not only do these so-called Independents want the trappings of power, they also want to take away the limited resources afforded to the opposition."
Fianna Fáil Ard Fheis
Fianna Fáil members will vote later on the draft programme for government.
Party leader and Tánaiste Micheál Martin will address the Ard Fheis conference in Dublin ahead of a debate on the proposed governance plan.
The event is taking place just days before Tánaiste Mr Martin is due to become taoiseach for the second time.
While Fianna Fáil has organised a one-off conference to rubber stamp the programme for government, with the vote result to be announced on Sunday evening, Fine Gael is holding a series of five regional meetings, the last two of which will take place in Meath and Cork on Sunday afternoon.
The results of the secret ballots held at the Fine Gael meetings will be announced on Monday.
Tough Cabinet decisions ahead
Mr Martin and Mr Harris will face some difficult decisions ahead of the return of the Dáil on Wednesday, January 22nd, when their new government will be confirmed.
Reflecting Fianna Fáil's general election return of 48 seats to Fine Gael's 38, it is understood Fianna Fáil will have eight Cabinet seats while Fine Gael will have seven.
Mr Harris is set to become Minister for Foreign Affairs and Trade, and Tánaiste. It is believed one of his key briefs will be forging a relationship with Donald Trump's incoming US administration.
Another widely expected move will see Paschal Donohoe and Jack Chambers swap roles, with Mr Donohoe returning as Minister for Finance and Mr Chambers becoming Minister for Public Expenditure and Reform.
Darragh O'Brien is set to remain as Minister for Housing.
There is a vacancy in the Department of Health after Stephen Donnelly lost his seat in the general election.
Fine Gael Dún Laoghaire TD Jennifer Carroll MacNeill has been linked to this role.
Helen McEntee is likely to move from the Department of Justice, and there are a number of contenders for that role. Frontrunners are understood to be Fianna Fáil's James Browne and Jim O'Callaghan.
Both Mr Martin and Mr Harris will be reluctant to demote any of their current Cabinet ministers, meaning the decisions will be difficult.
Along with Ms Carroll MacNeill, Mr Browne and Mr O'Callaghan, the likes of Neale Richmond (Fine Gael), Mary Butler (Fianna Fáil), Alan Dillon (Fine Gael), Niamh Smyth (Fianna Fáil) and Timmy Dooley (Fianna Fáil), are all understood to be candidates for promotion.
This means there will be a number of people disappointed, regardless of how the roles are divided.
Abroad
In the US, all eyes are on Donald Trump's inauguration in Washington DC on Monday, which has been moved indoors to the US Capitol building due to freezing temperatures.
Mr Trump's huge immigration crackdown may begin as soon as Tuesday, with Chicago reportedly the first target.
In the UK, all eyes are on chancellor Rachel Reeves as the economy continues to take big hits.
The UK's borrowing costs have hit record highs, but Ms Reeves has said this is a global phenomenon.
