Here are those four areas - and what has happened on each subject since the Singapore summit.
1) "The United States and the DPRK commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity."
"Peace and prosperity" are certainly lofty goals, but it's not clear what working towards them means in practice.
After the Singapore summit, attempts to establish US-North Korea working groups ran into difficulties. Secretary of State Mike Pompeo struggled to make progress in his meetings with North Korean counterparts, while Stephen Biegun, the US special envoy to North Korea, initially struggled to get meetings with North Korean officials at all.
There have been some signs of progress here in recent months. Notably, Biegun has been able to meet his North Korean counterparts since the second summit was announced. The two sides have also mooted opening liaison offices in each other's countries - a possible step towards formal diplomatic relations.
But US-led bilateral and multilateral sanctions on North Korea remain in place, much to the chagrin of Pyongyang. The US Government is still demanding progress on denuclearisation before those sanctions can be lifted.
2) "The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula."
This vague statement overlapped a lot with the first, but the mention of a "peace regime" was important.
A peace regime means a formal end to the Korean War. That conflict ended in 1953 with an armistice, but an official peace was never reached. The peninsula technically remains at war, and the demilitarised zone (DMZ) between the two Koreas is still one of the most tense borders in the world.
While North Korea has long wanted a formal end to the war, previous US administrations have argued that such negotiations could happen only after Pyongyang gives up its nuclear weapons. But there is widespread speculation that Trump may announce that he intends to end the war or even agree to a peace treaty.
Either of those options would be complicated. The other parties to the war, including China, would need to be involved. A peace treaty could also require the consent of Congress, which might balk at a measure that could undermine the argument for keeping US troops in South Korea.
In the meantime, there have been some positive steps. Increased inter-Korean cooperation has led to a more peaceful atmosphere on the peninsula, and South Korea has removed some military positions near the DMZ. The United States and South Korea have also suspended a number of joint exercises in what the Pentagon's chief spokeswoman has described as a move "to give the diplomatic process every opportunity to continue."
3) "Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work toward complete denuclearization of the Korean Peninsula."
When Kim first met his South Korean counterpart, Moon Jae In, last April, the two leaders signed a declaration that they would work towards "a nuclear-free Korean Peninsula." Trump and Kim reiterated this aim at their Singapore summit.
But the meaning of "complete denuclearisation" isn't necessarily obvious. The US views it as the "complete, verifiable and irreversible" end of North Korea's nuclear programme. But North Korea may have a broader definition that includes the removal of nuclear-armed American bombers and submarines from the area - or even the removal of all US troops from South Korea.
There has been some progress on North Korean nuclear weapons recently. Pyongyang hasn't tested a nuclear weapon since September 2017, and its last missile test came a month later. It also destroyed Punggye-ri, a nuclear testing site, in May 2018. But these were unilateral moves that took place before Trump and Kim met. There has been little action since then. And while North Korea isn't overtly testing weapons, it may still be producing them.
4) "The United States and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified."
The agreement to let the United States recover the remains of US troops from the Korean War was the least ambiguous of the Singapore aims - and perhaps the most successful. Fifty-five sets of remains were returned in a ceremony in July.
But the US would like to receive more remains from North Korea, and for American researchers to be allowed into the country to search for remains, as they were in the past.
In a statement released last week, the Coalition of Families of Korean & Cold War POW/MIAs - an organisation that brings together families of US troops lost in foreign wars - said that negotiations to resume joint operations had "stalled" and that "remains of US servicemen already exhumed in the DPRK wait to be returned."
