Here's a reminder of what's at stake, and what to expect over the next few days and weeks.
The story so far
The general election on March 4th left Italy with a hung parliament, as most observers had predicted. There was a slump in support for the governing centre-left Democratic Party (PD), and a rise in votes for the populist Five Star Movement (M5S), which emerged as the largest single party, though the centre-right coalition came out on top as the largest bloc overall.
It was within that coalition that the biggest upset occurred. Though Silvio Berlusconi had put the bloc together, it was his ally Matteo Salvini's League party that received the most votes, and since then, Salvini has been keen to assert his position as leader of the rightwing group.
One sign of progress was the election of speakers for both houses of parliament. The M5S' Roberto Fico, was elected speaker of the lower house, the Chamber of Deputies, while Forza Italia (FI)'s Elisabetta Alberti Casellati, representing the centre-right coalition, was elected head of the upper house, the Senate.
However, the parties are no closer to a deal when it comes to forming a government.
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Talks on Wednesday and Thursday are just the beginning of what could be a long process.
On Wednesday, Italian President Sergio Mattarella will speak to the speakers of Italy's two houses of parliament, his own predecessor Giorgio Napolitano, and the representatives of Italy's autonomous regions and smaller political groups.
The following day, it will be the turn of the major parties: the Democratic Party, Forza Italia, League, and Five Star Movement.
On the right, there's Matteo Salvini. His prominence is likely to send jitters through markets and the EU, but it's worth bearing in mind that Salvini is not the League. Though many of his own views are on the extreme right of the political spectrum, the League -- formerly known as the Northern League -- was created with the goal of achieving autonomy for Italy's northern regions, meaning its politicians and supporters come from both the left and right.
Leading the Five Star Movement is Luigi Di Maio, a relative political newcomer who has toned down the party's radical stance regarding the EU and possible deals with traditional parties. Though the party positions itself as 'anti-establishment' and refused to join a coalition, it has said it is ready to talk to all parties after the vote. On the eve of the government talks, however, Di Maio added a caveat, telling a TV interview he would not do a deal with Silvio Berlusconi's Forza Italia party.
Another name you'll be seeing a lot is that of Italian President Sergio Mattarella. During the day-to-day running of Italian politics, the president's role is low-key and largely ceremonial, but in these consultations he becomes one of the central players. He's the man with the mandate, and will have the job of naming Italy's next prime minister.
While all this is going on, it will be outgoing Prime Minister Paolo Gentiloni who will continue to preside in a 'caretaker' role, despite having officially tendered his resignation.
Photo: Alberto Pizzoli/AFP
The talks could last for weeks. It all depends whether and when a large enough portion of the main parties are able to make an agreement, and whether Mattarella can be convinced that they could form a workable government.
A government led solely by either the M5S or centre-right bloc is improbable, given that both groups are dozens of seats short. So an alliance of some form is more likely. But with M5S now refusing to govern with FI (which in any case is hostile to the M5S), the League refusing to govern with the PD (which has vowed to remain in opposition, despite the M5S suggesting it would be open to a deal), it's hard at the moment to see how that would work.
The League is unlikely to ditch Forza Italia to govern with the M5S, since this would relegate Salvini to a junior ally once again. If the two biggest parties did join together, the result would likely be an uneasy coalition. Many of the League's supporters want autonomy for the north, while the M5S has most support in the neglected southern regions, and it would be hard to find a compromise regarding the parties' policies on tax and welfare (the M5S supports a 'basic income').
If no government can be formed after several rounds of talks, Mattarella has two options. He isn't restricted to giving the job of PM to one of the party leaders and could instead pick a technocrat or political outsider, allowing them to form a grand coalition drawing support from across the political spectrum.
The president may also call another general election, which would likely take place before the end of the year. If this is the case, an interim government (probably either a large coalition, or a M5S-League government with a limited mandate) would be given a limited mandate, possibly including the task of rewriting the electoral law in order to produce a majority in the next vote.