The oil ban agreed by the European Union, which will be phased in over a period of months to try to reduce the impact on some of the weaker European economies, is the most significant toughening of sanctions to date.
The EU is also to bring in restrictions on the Central Bank of Iran and to expand a range of other existing measures intended to constrain Iran's ability to do business abroad.
The new sanctions, coming just as a US naval flotilla accompanied by British and French warships is testing the freedom of passage in the Strait of Hormuz, are inevitably going to ratchet up tensions.
They raise a host of fundamental questions. What impact will the oil ban have? Is there any chance that it will encourage Iran to halt its uranium enrichment programme? And if not, could the sanctions instead bring the various parties closer to some kind of military or naval clash?
Europe accounts for about 20% of Iran's oil exports.
Greece is heavily dependent on Iran, from which it buys about one third of its oil.
Italy and Spain each buy a little over 10% of their oil from Tehran. They will all now have to seek supplies elsewhere.
The ban is to be phased in to minimise disruption. And it looks pretty clear that other suppliers like the Saudis - despite Iranian threats - are willing to step up to cover the additional output required.
Nobody of course wants to see an oil crisis that might set prices spiralling.
Iran's customers in Europe are among the weakest economies in the EU. And any significant price rise would only benefit Iran's exports elsewhere.
Of course Iran's major customers are not in Europe but in Asia.
It is here that the fate of this sanctions round will be determined. The US has sought - so far with only limited success - to persuade South Korea and Japan to scale back their imports of Iranian crude.
China, which buys over one fifth of Iran's oil, is clearly the key. It is sending conflicting signals.
On the one hand, it appears to have significantly cut back on orders from Iran and sought to bolster its ties with other Gulf producers.
However, it is by no means clear if this is a desire to warn Iran diplomatically or a manoeuvre intended to strike the hardest bargain once the Iranian oil sector is under pressure.
So once the new measures are in place, how successful will they be?
Even Western diplomats are uncertain. There is no doubting that the Iranian economy will suffer. But the nuclear programme is a matter of national pride and ultimately national security.