Then there is a warming planet under attack by recent natural disasters and how to handle Mr Trump's plans to withdraw from the Paris Climate Change agreement.
Leaders' week at the United Nations brings together more than 100 heads of state and governments, but one undoubtedly stands out -- Donald Trump.
The US President has showed signs of softening his fierce criticisms of the international body, but its ability to address the current critical issues will come under close scrutiny.
At the top of the U-N's busy agenda this week is what Secretary-General, Antonio Guterres, has described as "the most dangerous crisis that we face today".
Mr Trump has been leading the condemnation of North Korea and in his first address at the General Assembly he's expected to rally support from the other nations.
Foreign Minister, Julie Bishop is there representing Australia.
North Korea is significantly the big issue here and is the subject of much discussion in bilateral meetings and side meetings, and so I expect much of his speech be dedicated to how to deal with North Korea, because the United States has led the Security Council in imposing very tough economic sanctions on North Korea. These sanctions must be given time to work but the United States has been quick in calling for political and diplomatic and economic pressure on North Korea, so expect much of his speech will be about North Korea.
The U-S Ambassador to the UN, Nikki Haley has already signalled that the Security Council has run out of options and the Pentagon may be called to step in.
What that intervention may look like, is slowly being revealed.
Defence Secretary, Jim Mattis is reportedly proposing that a military solution that would avoid any counterattack is possible, but has not gone into the details of what that could involve.
A clear international response to the Rohingya crisis is also being considered, with British Foreign Secretary, Boris Johnson, hosting a ministerial meeting.
"What we're trying to get everybody to agree, is number one, the killings have got to stop and the violence has got to stop. And we look not just to the military but also to Daw Suu to show a lead on that. Number two, humanitarian aid has got to be allowed through. And obviously we want to see the Rohingya allowed to come back with a minimum, minimum let or hindrance of the Rohingya population have got to be allowed to come back. I think about a third of the Rohingya population of Rakhine have been driven from their homes. It's an absolute catastrophe and that cannot be allowed to stand."
Ms Haley and Ms Bishop were part of the meeting along with Turkish Foreign Minister, Mevlut Cavusoglu, who had visited the region earlier this month.
"We saw the living conditions and we need to support the state and government of Bangladesh as well, as those vulnerable people living in difficult situations. Humanitarian aspects and a political solution."
One issue that has received backing is a plan to fight sexual exploitation, with the Prime Minister of Bangladesh, Sheikh Hasina meeting with applause her commitment of a $100,000 (US) dollars as a token contribution to the victim support fund.
Last year, 195 countries signed the Paris agreement, in a display of near unaniminity.
But the threat of a U-S withdrawal has placed climate change firmly back on the agenda.
"Dear friends, you are the backbone of the global movement that led to the adoption of the Paris agreement in 2015. And in Paris, we rose to a global challenge, but now we have an even bigger challenge: raising ambition and staying on course. Emissions are going down, but not enough. The temperature is still rising. We see the consequences daily. We count the costs in lives, livelihoods, damaged economies. And since 2008 - and you know better than me - some 20 million people a year have been forcibly displaced by floods, storms, fires and extreme temperature. But many more are on the move due to droughts and sea level rise and climate change is not a distant problem for future generations. It is here, it is now, and we need to deal with it."
French President, Emmanuel Macron is among the leaders vocal in wanting Mr Trump to reconsider his position.
He met with the U-S President with this intention in mind.
But speaking before their meeting, Mr Trump seemed more interested in how to replicate the fanfare of his counterpart's national day.
"I do want to say that I was your guest at Bastille Day and it was one of the greatest parades I have ever seen. It was two hours on the button and it was military might and, I think, a tremendous thing for France and for the spirit of France. And to a large extent because of what I witnessed, we may do something like that on July 4th in Washington down Pennsylvania Avenue, if I have your approval. I don't know. We're going to have to try and top it - but we got a lot of planes going over, a lot of military might."
