What has led to the request for statehood?
Palestinians have been fighting for their own sovereign state on the West Bank and Gaza since their occupation by Israel in 1967.
Peace talks and negotiations have been running for decades but a solution to satisfy both parties has never been found.
In a shift last year, Palestine started asking countries to recognise an independent state based on 1967 borders.
To date it has only had observer status at the UN but now Mr Abbas is asking for admission as a full member state.
Significantly this could give the region access to the International Criminal Court where they could challenge the Israeli occupation.
How does the application work?
Mr Abbas has to submit a written application to UN secretary-general Ban Ki-moon for approval.
If this is granted, the UN Security Council will then look at the application and pass a vote.
Palestine will need nine of 15 council members to support their move - and crucially no vetoes from permanent members.
China, France, Russia, the UK and the US are all permanent members who enjoy this right of veto.
The 10 non-permanent members, who sit for two-year terms, are currently Bosnia and Herzegovina, Germany, Portugal, Brazil, India, South Africa, Colombia, Lebanon, Gabon and Nigeria.
On approval by the Security Council, the application would then need a majority of two-thirds in the General Assembly to stand.
However, US President Barack Obama has already declared he will use his veto, which means it is unlikely to reach this stage.
Are there any alternatives?
One option would be to give Palestine enhanced status as a non-member state, a position held by the Vatican.
For this, only a simple majority in the UN General Assembly is needed and importantly no country has a veto.
A vote could be held almost immediately, but it is expected it would be delayed to allow time for negotiations over the wording.
Being a non-member state could still let Palestine take Israel to the International Criminal Court, a threat which could increase their leverage in negotiations.
Another possibility is for the Security Council to delay any action on the request, allowing the mediating Quartet more time to draft a declaration aimed at coaxing both sides back to the table.
The US, Russia, EU and UN have been working on a statement for months but have yet to produce the document.
Any agreement would have to directly address possible borders and Israel's insistence it be recognised as a Jewish state.
Even if diplomats can agree among themselves, it is unclear whether Israel and Palestine will agree to restart negotiations.
What would a resolution say?
If the Security Council route fails, Palestine could ask the General Assembly for admission as a non-member observer state.
It might also acknowledge the countries that have recognised Palestine's statehood and an appeal for full UN membership.
There might also be requests about the peace-making process and an outline for re-starting negotiations with Israel.
Would becoming a state change anything for Palestine?
The move would be mostly symbolic because the 1967 borders are already widely regarded as the best basis for a peace settlement.
However, the situation is at an impasse because Israel refuses to accept the prospect of an agreement along these lines.
Israeli Prime Minister Benjamin Netanyahu described the prospect as "indefensible" when it was tabled by US President Barack Obama back in May.
The Palestinians hope that admission as a full member state would give them more weight in any negotiations.
But Mr Obama has insisted this week that there is no "short cut" to peace and the situation has to be resolved through talks with Israel.
Where does Israel stand?
Israel insists peace can only be established through negotiation and has warned that the UN bid could seriously damage the peace process.
Israeli Prime Minister Benjamin Netanyahu refuses to enter negotiations with pre-conditions about 1967 borders, arguing a return to that arrangement would expose its heartland to rocket fire from the West Bank.
What is the potential fallout?
Applying to the Security Council or getting a UN Assembly vote could have considerable consequences for the region and the wider world.
Some Israeli politicians have threatened the annexation of parts of the World Bank and others have threatened to withhold taxes it collects on behalf of the Palestinian Authority.
There is also the possibility that demonstrations in the West Bank will escalate, with renewed violence and clashes.
Israeli and US politicians have threatened financial reprisals that could cripple the Palestinian Authority in a bid to deter Palestine.
One Abbas aide has said that if that does happen, the PA could dissolve itself and force Israel to reassume responsibility for the whole of the West Bank, which would be a major demographic and security liability.
For the US, exercising its veto would also lose Barack Obama what little credibility he has left in the Arab world.
His administration has already been seen as a reluctant supporter of the Arab spring and risks being seen as on the wrong side of history.
How will events unfold at the UN?
Palestinian leader Mahmoud Abbas will address the UN General Assembly later, setting out his case for statehood.
Israeli Prime Minister Benjamin Netanyahu will take to the podium immediately afterwards to argue that only direct negotiations can lead to a Palestinian state
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