But there are failures too. India, Pakistan, North Korea, and probably Israel, have developed nuclear weapons despite the NPT, Russia is teasing the prospect of nuclear war and nuclear states like the UK, that had previously been relied on to bang the disarmament drum are now talking about increasing their arsenals.
The Bulletin of the Atomic Scientists' annual Doomsday Clock, an academic marketing exercise that reckons how close humans are to man-made apocalypse, is set at 100 seconds to midnight - closer than at any point in our history.
Twyford is realistic about progress.
"It's been a tough time for nuclear arsenals in recent years. Progress has stalled if not reversed," he said in an interview with the Herald before leaving for New York.
Twyford is there to take part in the review of the NPT because "the world needs it".
"Since 1968, it has played a very important role in preventing the spread of nuclear weapons. Not entirely successfully, but largely," Twyford said.
"And until the TPNW - the ban treaty - the NPT has been the main bit of international law the world has looked to for the disarmament and elimination of nuclear arsenals," he said.
Twyford is the Disarmament and Arms Control Minister, a portfolio established when New Zealand went nuclear free in 1987. The role was by junked by National in 2011, but revived by Labour in 2018 and given to Winston Peters. Twyford has been in the chair since 2020.
The TPNW, or The Treaty for the Prohibition of Nuclear Weapons is the other major international treaty Twyford looks after. Signed in 2017, it calls for the outright prohibition and swift abolition of nuclear weapons. No country that possesses or hosts nuclear weapons can be a signatory, and those that do, must commit to a swift disarmament.
It won't achieve disarmament overnight, but its 86 signatories and 66 parties hope it will keep up the pressure on nuclear-armed states to disarm. New Zealand is an active member of this agreement too, and Twyford travelled to Vienna this year to deliver a speech for the first meeting of parties to the agreement.
Twyford reckons progress towards disarmament was looking up a decade ago, when US President Barack Obama and Russia's Dmitry Medvedev showed some will to push towards disarmament.
"Obama's Prague Speech [2009] gave people hope that for the first time since Reagan and Gorbachev we were going to see some political will on behalf of the US and Russia," Twyford said.
But Obama gave way to Donald Trump, and Medvedev turned out to be simply keeping the seat warm for current President Vladimir Putin who was on a brief, constitutionally mandated sabbatical during Medvedev's single presidential term. Now, disarmament ambitions are in tatters.
"The nuclear weapons states are investing large amounts of money - 100 millions if not billions of dollars in the modernisation of their arsenals.
"All the old agreements and treaties have fallen by the wayside. We've seen China investing massively in expanding its arsenal. The British, who were among the most transparent of nuclear powers, are reducing the cap they had committed to as part of their arsenal [increasing the number of warheads they hold]," Twyford said.
"We are at more danger now in terms of catastrophe than at any point since the Cuban Missile Crisis," he said.
While nuclear weapons states are rearming, disarmament appears to be becoming a more significant part of New Zealand's foreign policy. Prime Minister Jacinda Ardern used much of her three minutes at the Nato summit in Madrid this year calling on states to disarm - a slightly awkward intervention given the nuclear deterrent is a central plank of Nato's collective defence policy.
In that speech, she made a direct plea to Nato states to use the NPT's meeting to recommit to disarmament.
"I also come with a request: that we do not allow the legacy of the war in Ukraine to become an arms race, or an even more polarised and dangerous world," she told the conference.
Our solidarity with Ukraine must be matched by an equal commitment to strengthen international institutions, multilateral forums and disarmament.
"As the Nuclear Non-Proliferation Treaty convenes for its tenth review conference in August, I hope all members agree to send a strong message. Because if not now, when the threat is even greater, then when?" she said.
Disarmament was also mentioned as a "priority" in Ardern's major foreign policy speech at the Lowy institute in Sydney last month.
Despite the pessimistic backdrop, there's some optimism. Twyford noted US President Joe Biden came into office with a new commitment to New Start, a US-Russia nuclear weapons reduction treaty, which was extended last year, and the Strategic Stability Dialogue, a commitment to predictable relations between the two countries that is meant to reduce the risk of nuclear war.
Despite these efforts, however, the war in Ukraine seems only to have brought the threat of nuclear war closer, thanks to Russia's threats, and this has only served to whet the appetites in the West for further nuclear armament.
This makes New York tricky. Twyford said New Zealand will continue to condemn all nuclear threats, but New Zealand also needs Russia at the table to further the disarmament agenda.
He said New Zealand wants "nuclear weapons states coming to New York serious about nuclear disarmament".
Twyford said there were like-minded allies in Thailand, Indonesia, Egypt, South Africa, and Nigeria.
But any breakthrough would probably be reliant on the two biggest nuclear powers agreeing to something between them, in much the same way the US and China's prior agreement on climate change paved the way for the signing of the Paris agreement in 2015.
"We should be looking to the US and Russia to make some kind of commitment to get around the table and undertake nuclear disarmament between the two of them and i think that would create the climate," Twyford said.
So far, there's been some hope on both sides.
Before the meeting, Putin repeated what had been said in January: "There can be no winners in a nuclear war and it should never be unleashed, and we stand for equal and indivisible security for all members of the world community," he said.
On Tuesday, New Zealand time, Twyford attended a meeting with US Secretary of State Antony Blinken.
In a published speech, Blinken said that while the NPT had made the world safer, it was "increasingly under strain".
Blinken added Russia's invasion of Ukraine sent the "worst possible message" to countries trying to disarm, which was that nuclear armed states were more easily able to pick on countries without nuclear weapons - and in Ukraine's case, a country that had given up those weapons.
Biden also said he was "ready to expeditiously negotiate a new arms control framework" to replace New Start, the agreement between the US and Russia, when it expires in 2026.
"Russia should demonstrate that it is ready to resume work on nuclear arms control with the United States," he said.
Twyford said the statement from Biden got the conference "off to an encouraging start".
"That's exactly the sort of leadership the NPT needs right now and we hope other nuclear weapons states will follow suit," Twyford said.
