Taoiseach Micheál Martin is settling into his new position in the midst of a global pandemic and warnings that Ireland is facing the fastest-moving recession ever to hit the country.
There are a number of issues hurtling towards the new coalition from day one - here are five of the biggest challenges facing the new Government.
The fallout from Covid-19
This is the biggest challenge facing the new coalition. A key priority will be managing the crisis and minimising the impact on the health of the State.
Although the virus is largely under control in the community, the threat of a second wave is ever present.
As Ireland reopens from restrictions imposed to flatten the curve of infection, more people will be in closer contact, thus increasing the possibility of a rise in infections.
Keeping the country open and managing this risk will be a fine balancing act for the new Government.
One of its first challenges will be deciding what to do about people who want to travel outside the country on foreign holidays.
Airlines have been marketing cheap flights while the Government has been advising people to avoid all unnecessary trips overseas.
Restrictions on international travel, which were expected to be eased on 9 July, are now set to remain in place until 20 July at the earliest, under plans to be considered by the Cabinet on Monday.
Debt, deficit and the interest bill
As large parts of the economy reopen, the scale of the damage done by Covid-19 will become apparent.
The challenge for the Government is to restart the economy and get investment going again. Saving jobs and businesses will be the first economic priority for the new administration.
With many small and medium businesses crying out for a cash injection to keep them afloat, the new government needs to urgently pass legislation to bring forward a €2bn scheme of credit guarantees for companies.
A second wave of the virus would be hugely damaging to the economy. There was a stark warning from the Central Bank this week, which said the economy could shrink this year by up to 14%.
The Government has said it will borrow its way out of the crisis. But there is a risk that interest rates, which have remained very low in recent years, could rise.
The Secretary General at the Department of Public Expenditure and Reform, Robert Watt, told the Covid-19 Committee that if public debt rose to €250bn, an interest rate of less than 2% would generate a bill of between €4-5bn.
However, if that rate jumped to 4% that interest rate bill would double to €10bn per year.
The Government will unveil its stimulus jobs package over the coming weeks. The aim is to help reduce the 900,000 people now in receipt of welfare income supports.
The package could include support for SMEs, improving grants for business and targeting thousands of young people out of work.
The Government also face the task of phasing out the Pandemic Unemployment Payment and the Wage Subsidy Scheme, which will be economically and politically difficult, and whether to extend the Covid-19 payments and for how long.
For the second time in ten years, the country is facing a recession and politicians will inevitably have to make some difficult decisions.
The big challenge for the new coalition will be trying to bring the public finances into balance over the coming years.
The new administration will hope to have a better picture of the size of the budget deficit, which could run to €30bn, when the Budget is announced on October.
Happy families ... making the coalition work
Fianna Fáil and Fine Gael joining forces in a coalition Government was a watershed moment marking an end to a political feud dating back to the foundation of the State a century ago.
Both parties will have to put their past differences aside and work together, while ensuring they keep their own identities at the same time.
There is also the added challenge of working with the Green Party, which made reducing carbon gas emissions by 7% annually a cornerstone of its conditions of entering coalition.
Differences in opinions between the parties over the impact of cutting emissions on agriculture will be a tricky issue.
Smaller parties traditionally suffer in coalitions and the Green Party will be pushing to make its mark in this administration.
Adrian Kavanagh, lecturer in Electoral and Political Geography at NUI Maynooth, said communication between parties will be critical.
"Communication is the main thing where coalitions have fallen down in the past, when both sides break down and they stop trusting each other," he said.
"It has a lot has to do with personalities, to be honest, and it doesn't matter how you have gotten on with different people in the Government.
"The three most important people are Leo Varadkar, Micheál Martin and Eamon Ryan. If they can get a good working relationship between them over the next two years it bodes well for the coalition."
In their first week, Minister Varadkar told the Dáil that the leaders of the three coalition parties had not coordinated the make-up of the Cabinet "as well as they might have".
This led to a backlash over Fianna Fáil TD Dara Calleary’s appointment as chief whip, with some arguing he deserved a full ministry.
Another issue will be how the three parties deal with defections.
The Government has a fairly comfortable majority with 84 seats and enjoyed the support of nine independents in the vote for Taoiseach last weekend.
But it faces tough economic decisions and the Green Party will have to work to manage the anti-coalition camp within the party.
Fianna Fáil has also had to manage disappointment on the back benches about decisions made on junior and senior ministries, which could cause problems for the Taoiseach.
Micheál Martin also has to be awake to Jim O’Callaghan’s decision to turn down a junior ministry. Some observers interpret that move as an indication of Mr O’Callaghan’s leadership ambitions.
Threat of a no-deal Brexit
The possibility of a no trade deal Brexit has not gone away and has been somewhat overshadowed by the coronavirus pandemic.
The British government has ruled out seeking an extension to the transition period, which allows the UK continued access to the EU single market while trade talks take place.
Without a trade deal, Brexit could further impact businesses in Ireland already struggling to deal with the fallout of Covid-19.
The new Government has the advantage of the continuity of Fine Gael ministers who have been involved in Brexit negotiations from the beginning.
However, if there is no trade deal Ireland could be doubly hit by it and the economic fallout from the pandemic.
Health service and getting waiting lists down
The coronavirus outbreak has put huge strain on the health service with mounting waiting lists.
Capacity issues in hospitals were a problem in Ireland for a long time before the pandemic hit the country.
Infection control measures that are now required because of Covid-19 mean capacity in hospitals has plummeted even further.
The new Minister for Health Stephen Donnelly will have his hands full trying to address this issue.
Thousands of people across the country are waiting months, or in some cases years, to see a doctor or access a scan, treatment or surgery.
Minister Donnelly has indicated that he wants to accelerate Ireland's move towards universal healthcare and has said the Sláintecare plan is still the main route to reform.
The Fianna Fáil Minister made a number of promises while on the opposition benches and will be under pressure to deliver in his first few weeks and months in Government.