The Senate now has a record number on the crossbench, with 18 senators not aligned with either the government or the opposition.
The upper house has a total of 76 senators and 39 votes are needed to pass legislation.
Labor and the Greens together have held the balance of power since 2010, with 31 and nine senators respectively.
Both major parties lost senators in the recent election, which will see 18 crossbenchers in the upper house. It’s the highest number on record, up from the previous high of 13 crossbenchers in 2002 to 2005.
With a total of 33 senators, the Coalition will need the support of six crossbench senators to pass legislation. With 25 senators, Labor will need support of 14 to secure a vote in their favour.
The incoming Senator-elects
They've been variously described as 'ragtag, mishmash, flotsam and jetsam', but these are the people who will decide the legislative future of Australia.
The new Senate will have 18 crossbenchers, meaning the Abbott Government will need to undertake continual negotiations to gain the 39 votes needed to pass bills in the upper house.
Click on the image above to read more about the incoming Senator-elects and listen to complete interviews.
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Upcoming legislation in the Senate
It appears likely that the repeal of the carbon tax will be among the first bills passed by the new Senate following significant negotiations with the Palmer United Party.
Party leader and Member for Fairfax Clive Palmer has agreed to back the repeal on the proviso that the Clean Energy Finance Corporation and the Climate Change Authority are retained.
The government has also indicated it will take “strong action” to ensure energy companies pass on savings from repealing the carbon tax to consumers, another of Mr Palmer's requests.
Mr Palmer is pushing for an emissions trading scheme, though Opposition members are concerned that the country could be left without any climate policy.
The vote is expected to come before the Senate within the fortnight and Prime Minister Tony Abbott has told media he is taking nothing for granted.
The repeal of the carbon tax also has the support of incoming Queensland LNP Senator Matthew Canavan, who described it as “one of the key reasons” he got into politics.
NSW Liberal Democrats Senator-elect David Leyonhjelm is also supporting the repeal and a PUP push to axe the Coalition’s Direct Action, which he says is “$2.5 billion which won’t make any difference to climate change”.
Mr Leyonhjelm is also voicing support for the Abbott Government's cuts to welfare, saying he was "broadly sympathetic" to their objectives.
"We are living beyond our means," he said.
"There are way too many people receiving welfare that don’t deserve it… We do need a good safety net for those who are out of luck, but we can’t have 8 million people who are out of luck. It just doesn’t compute."