With all the votes finally counted, the scale of the left-wing, Irish nationalist party's surge is clear -- breaking a century of dominance by establishment heavyweight parties (Fine Gael and Fianna Fail) and changing the political landscape of Ireland, likely forever.

Here's what you need to know.

Is it correct to say that Sinn Fein won the election?

Sinn Fein won the popular poll, pulling in 24.5% of first-choice votes. But the party were pipped at the post by Fianna Fail, who netted 38 Teachta Dala (or members of parliament), to Sinn Fein's 37, thus making them the largest party by number of seats. Had Sinn Fein fielded more candidates in some constituencies they would likely have emerged the outright winner.

Could Sinn Fein form a government?

Technically Sinn Fein could form a government. There are a number of paths to this, none are easy and some are very improbable. One would be a coalition with Fianna Fail and some independent lawmakers, but there is little political crossover and much animosity. Sinn Fein President Mary Lou McDonald has talked about an alliance of left-leaning parties. To pull that off without Fianna Fail, she would need the backing of most, if not all, of the smaller parties and the independents to hold a majority. There are 160 seats in the Dail, 73 of those are taken by Fianna Fail and Fine Gael, and the path to a sustainable and successful government is challenging. Fine Gael, meanwhile, have rejected any alliance with Sinn Fein.

Does that mean Ireland could get its first woman Taoiseach?

It's not impossible, but at this stage it's unlikely. As the final votes were being counted, Sinn Fein seemed to float the idea of a rotating premiership. No details were available on how that could work or who would be involved in the rotation. One potential dampener on McDonald becoming the first woman Taoiseach is Fianna Fail's Michael Martin -- this election is perhaps his last chance to be Ireland's leader and he is unlikely to let that ambition die easily.

Why is Sinn Fein so controversial?

Sinn Fein appeared to have pulled off a major rebranding, seemingly burying their past as a party long accused of aligning with terrorism and violence.

Sinn Fein, although they repeatedly denied it, were the political wing of the IRA (the Irish Republican Army), who fought a bloody three-decade military campaign to throw the British out of Northern Ireland and unite the island of Ireland.

What were "The Troubles?"

The violence was known in an oddly understated way as "The Troubles," yet more than 3,500 people died and many more had their lives irrevocably changed.

The IRA was at the forefront of the conflict -- killing, bombing, shooting and intimidating their way to influence. They had grown out of a demand for equality in Northern Ireland's deeply bigoted society that often gave advantages to Protestants over Catholics.

As one of Sinn Fein's early politicians said -- they would rise through the Armalite [gun] and the ballot paper.

How has Sinn Fein rebranded itself and is it really a different party?

The moment Northern Ireland's Good Friday Agreement was signed in 1998, Sinn Fein President Gerry Adams pivoted south of the border rather than take a plum job in the north. He has always denied he was an IRA commander and saw that the political path to his years-long struggle for a united Ireland ran through Dublin. He has shaped the party accordingly, bringing in younger, less tainted politicians and leaders.

Two years ago, Adams stepped back as party president and did not run in this election after serving as a TD (or member of parliament) in Dublin for almost a decade.

The party surged through its grassroots activism around issues that captured voters' attention -- housing, homelessness and healthcare -- and their demands for change matured alongside a generation that never witnessed their violent roots. Even so, one of their first elected TDs this weekend was a former IRA member, whose supporters sang rebel songs at the count center to celebrate his success. Meanwhile in Waterford, Sinn Fein's David Cullinane, newly elected on a mountain of first preference votes defended his acceptance speech support of the IRA as a comment on "the past not the future." Non-Sinn Fein voters may be troubled to see that McDonald appeared to defend Cullinane's comments as a "distraction" from the important work of forming a government.

Are Sinn Fein's gains likely to have an impact on Brexit talks?

Absolutely. Sinn Fein are now the only Irish party with major political influence both north and south of the Irish border, the European Union's new land border with the United Kingdom. Such is the seismic shift in Irish politics that Sinn Fein's demand for a united Ireland will be heard louder.

This will drive up growing Unionist fears in Northern Ireland, so whether he likes it or not, UK Prime Minister Boris Johnson's Brexit considerations will have to deal with this reality. Perhaps more directly, an Irish government with ardently pro-united Ireland Sinn Fein inside of it, or even in strong opposition to it, could stiffen the EU's resolve on negotiations and therefore limit potential concessions to the British.

This story has been updated.