The five permanent members of the UN Security Council plus Germany (the P5+1) want Iran to scale down its nuclear activities in order to make any dash to make a bomb extremely difficult.
In return Tehran, which denies seeking to develop nuclear weapons, wants the lifting of UN and Western sanctions that are causing its economy major problems.
In July after months of intense talks, negotiators gave themselves four more months, until November 24, to strike a deal.
Now, with the latest extension, they want a framework deal by March 1 and a full agreement including all technical aspects by July 1.
Here is a look at the main issues:
ENRICHMENT: The thorniest problem is enrichment, the spinning of uranium gas at supersonic speeds in centrifuge machines to make it suitable for power generation and medical uses but also, at high purities, for a bomb.
Iran's supreme leader Ayatollah Ali Khamenei said in July that Iran wants to vastly multiply its enrichment capacities to industrial levels. But the powers want Iran to slash them. Both sides have called for more "realism" on this point.
PROGRESS: Progress has apparently been made in other areas. These include greater oversight for UN inspectors and a different use for Fordo, Iran's second main enrichment site in a bombproof bunker under a mountain near Qom.
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Another is Iran's apparent willingness to change the design of a new reactor it is building at Arak in order to ensure that it produces much less plutonium, an alternative to highly enriched uranium for a bomb.
TIMING: Apart from enrichment there are other tricky aspects, not least the duration of the mooted accord. Washington wants Iran's nuclear activities limited for a "double-digit" number of years. Tehran wants considerably less.
Another is the pace at which sanctions would be lifted and how to tie the relief to certain "milestones" reached by Iran. The lifting of sanctions by the UN Security Council and a sceptical US Congress controlled by the Republicans also presents legal difficulties.
SKELETONS IN THE CLOSET: Another potential stumbling block is the UN atomic watchdog's probe into the "possible military dimensions" of Iran's programme – alleged work on developing a nuclear weapon before 2003 and possibly since.
After years during which Tehran rejected these allegations out of hand, progress at last began to be made this year but Iran has still not provided information on two out of around 12 areas of suspicion to the International Atomic Energy Agency, three months after an August 25 deadline.
HIGH STAKES: Reaching a deal could improve Iran's antagonistic relations with the West, paving the way for cooperation in other areas such as fighting militants in Syria and Iraq from the Islamic State group.
It would also silence what US President Barack Obama in 2012 called the "drums of war". Neither Washington nor Israel, widely assumed to have nuclear weapons itself, have ruled out bombing Iran.
In addition it would be an important milestone in global efforts to halt the proliferation of nuclear weapons, and represent a significant foreign policy success for Obama.