What's happened since the election?
As you probably know, Sweden's September 9th election left neither of the two main blocs (the centre-left and the centre-right Alliance) with an absolute majority, and there was just one seat between the two. The Sweden Democrats were the third biggest group, meaning some form of compromise will be essential for a working government.
Parliament reconvened for the first time since the vote on Monday, with a roll call of the newly-elected members.
The other big task was electing the new speakers of parliament. Usually, these roles are given out to candidates from different parties based on their size in the new parliament, but because the two main groups are now almost neck-and-neck, that didn't happen this time.
The Moderate Party's candidate Andreas Norlén was voted into the job of speaker, with the roles of deputy speaker, second deputy speaker and third deputy speaker going to candidates from the Social Democrats, Left Party, and Centre Party respectively.
With the speakers elected and Löfven having resisted calls for his resignation, lawmakers took part in a confidence vote on the PM, and Löfven was ousted from the role.
What's the next step?
Speaker Andreas Norlén has the official task of putting forward a proposal for who should become prime minister. According to a government statement, he will begin talks with the parliamentary group leaders on Thursday.
The decision is usually made after a lot of cross-party talks behind closed doors, in order to ensure that the PM candidate has a good chance of actually forming a government backed by parliament. So far, parliament has always approved the first proposal.
In the meantime, Löfven will continue to lead a caretaker administration until a new workable government is found. This has the same power as a regular government, but is expected to take care only of day-to-day issues and things that can't be postponed.
READ ALSO: Everything you need to know about the Swedish election
The Green Party's Isabella Lövin and Stefan Löfven during the confidence motion. Photo: Anders Wiklund/TT
Who are the most likely PM candidates?
Many observers think Ulf Kristersson, the leader of the Moderate Party, will be the first choice, and he is the Alliance's top pick, as the leader of the bloc's largest party.
What if the first attempt fails?
The speaker has four attempts to get parliament to agree to a new prime minister, or at least convince enough MPs to abstain and not actively vote against the candidate.
If they fail to agree on any of the four proposals, a new election must be held within three months. However, this has never happened in Swedish history.
What's the role of the Sweden Democrats?
In the lead-up to the general election, a lot was made about the potential influence of the far-right Sweden Democrats, who according to many polls were on track to become the second largest party. That didn't happen, but they could still wield some influence.
Some of the top Sweden Democrats were critical after their candidate failed to be elected to any of the deputy speaker posts. Leader Jimmie Åkesson called the Moderate Party "weak" for not voting for a Sweden Democrat after the far-right party supported the Moderate candidate for the speaker position.
The Centre Party and Liberals have said they would quit the Alliance if the Moderates and Christian Democrats were to negotiate a deal – for example on immigration – with the far-right in exchange for their support.
Any other options?
Löfven said on Tuesday that the Social Democrats would never be a partner in an Alliance government, and that this would be "undemocratic". But it would be possible for the Alliance to reach a compromise with the Social Democrats on big political issues, such as the autumn budget.