BBC News Online takes a look at some of the key issues.
Where are the talks being held?
With a long history of suspicion and mutual distrust both sides agreed to meet at neutral venues.
The third round of talks was held in the Norwegian capital, Oslo, between 2 and 5 December.
Norway has been seeking to broker peace between the Tamil Tigers and Sri Lankan government for a number of years.
The preceding two rounds of talks were held in Thailand between 16 and 18 September, at a naval base in Sattahip, and between 31 October and 3 November at Nakhon Pathom, a riverside resort on the outskirts of Bangkok.
How much progress has been made?
The talks set out to:
consolidate a February 2002 ceasefire
set up provisional administrative arrangements
discuss a final political settlement.
In the first round the Tigers dropped their demand for a separate state and agreed to settle for regional autonomy.
The second phase, attended by senior military and political figures from both sides, took on more detailed security and development issues in the conflict areas.
Committees were set up to examine rehabilitation needs in war-hit areas, to push for military de-escalation and to look at political questions at the heart of the 19-year civil war.
And during the third round both sides crucially agreed to share power within a federal system in which the Tamils would have autonomy in the north and east of the country.
What have the Tigers been fighting for?
Until a ceasefire first declared in December 2001, the Tigers had been fighting since 1983 for a separate state for Tamils in Sri Lanka's north and east.
They argued that the Tamils are discriminated against by the majority Sinhalese population.
But, as peace talks progressed, the Tigers dropped their demand for independence and say they will now settle for regional autonomy - a major concession.
The government also gave ground - this was the first time it had agreed to share power with the Tamil Tigers.
What's the human and economic cost of the war?
The conflict has killed about 64,000 people, displaced one million and held back the island's growth and economic development.
Some estimates suggest that the government has spent up to 5% of gross domestic product on defence in recent years.
Sri Lanka's once successful tourist industry has also been badly hit by the violence.
How have the talks been possible?
Observers say battle fatigue had set in on both sides, and it was becoming increasingly difficult for the army and the rebels to find new recruits to fight a war that looked more and more unwinnable.
Prime Minister Ranil Wickramasinghe won parliamentary elections last December, promising an end to conflict.
His keenness to make peace gave Norwegian mediators a huge boost. They brokered a permanent ceasefire in February 2002.
Initial fears that the Tigers would use the truce to regroup militarily proved unfounded, and consistent Norwegian pressure finally brought both sides to the negotiating table.
And the impact of 11 September in refocusing the world on terrorism and cracking down on the financing of terrorist activities may also have been important.
The LTTE are proscribed as a terrorist group in many countries.
Is everyone in favour?
Government efforts have met some opposition from the powerful President, Chandrika Kumaratunga.
She accused Mr Wickramasinghe of giving too much away without securing a promise from the Tigers to renounce violence for good.
The government and rebels have tried peace talks several times, most recently in 1995, but they have always ended in renewed violence.
That often led to accusations by both sides of not being serious about peace.
What comes next?
Any changes to the country's constitution - as a transition to a federal structure will require - must be passed by the Sri Lankan parliament.
To do so the government will need a two-thirds majority, but it currently has only a slim majority.
So the reservations of President Kumaratunga and opposition parties about the extent of the concessions made by the government during the peace talks could become more important.
And any solution will face its real test once implemented on the ground.
A Tamil Tigers car with soldiers in 2004. 
The Liberation Tigers of Tamil Eelam, otherwise known as the Tamil Tigers, have told the BBC that they are prepared to fight back against Sri Lankan forces.

The vow follows reports that Sri Lankan forces are laying siege to the last rebel-held areas of the island. The Sri Lankan army have said that the "final battle" was underway and predicted that the Tamil rebellion is finished. There have been rumours that Velupillai Prabhakaran, the Tigers' leader since the conflict began, had fled in the face of the assault. But political leader B Nadesan denied this, telling the BBC that the claim was "malicious propaganda".

According to Reuters, analysts say that around 2,000 Tiger fighters remain in the face of the 50,000-strong government push into the north, which began in August 2006. Government forces captured Mullaitivu, the last stronghold of the Tigers, on Sunday. The Associated Press says that Tigers have been preventing civilians from leaving the war zone, with the government accusing them of using civilians as human shields. In turn, the government has declared a section of the territory to be a safe area for civilians but there have been reports of artillery fire and the United Nations say troops have been fighting in the area.

Lt Gen Sarath Fonseka of the Sri Lankan army was quoted by the AFP news agency as saying "the end of terrorism is near and we will definitely win". Meanwhile aid agencies say 230,000 Tamil refugees are in the remaining battle zone. The Associated Press say that the area is densely populated and diplomats have expressed concern about the use of ground troops in the area. Most journalists are forbidden from entering the war zone, making confirmation difficult.

Sri Lankan President Mahinda Rajapaksa won the 2005 election on a hard-line ticket, ruling out autonomy for the Tamil north and east. This led to an increase in the war and the eventual abandonment of a Norwegian-mediated ceasefire at the start of last year.