Fixing the world economy, tackling the conflicts in Syria and Ukraine, and boosting global trade.
Point of view
It would be a pretty ambitious programme for any government over a number of years.
But the leaders of the G7 club of nations will be taking on all of them in Japan over the next two days.
The host country will be joined by the United States, Britain, France, Italy, Canada, Germany.
Donald Tusk and Jean-Claude Juncker, the two most senior EU officials will be there.
Expect some more of those awkward three-way handshakes, which have become a feature of official gatherings of this kind.
Neither China nor Russia are on the guest list. But both will be on the agenda.
Russia was suspended from the then G8 in March 2014 over the annexation of Crimea.
The Global Economy
The biggest issue will be how to breath life back into the global economy amid a slowdown in China and other emerging markets.
Other concerns weighing on the world economy include the UK’s possible withdrawal from the European Union and sluggish growth in the eurozone.
In April, the IMF cut its global growth outlook for 2016 from 3.4 to 3.2 percent, citing concerns over the Chinese economy and how emerging markets were being hit by a fall in commodity prices.
Japanese Prime Minister Shinzo Abe will call for the other G7 nations for more government spending, cutting interest rates and printing money to buy government bonds as a way of boosting growth.
The yen hit an 18-month high against the dollar at the start of May, making exports more expensive.
The United States put Japan on its currency watch list in April and warned against any further intervention to weaken the yen. A G20 agreement in St Petersburg in 2013, which includes Japan, said member nations would “refrain from competitive devaluation.”
And the Japanese hosts seem unlikely to win over German Chancellor Angela Merkel as her finance minister explained last week.
“The strategy of stimulating the economy with borrowed money quickly loses steam – it’s like setting straw on fire” said Wolfgang Schauble in an interview with the Japanese business daily Nikkei earlier this month.
“It’s important that we promote structural reforms and cut public debt, rather than use fiscal policy to stimulate growth,” he added.
The issue was unresolved at a meeting of G7 finance ministers last weekend. It means the G7’s leaders carefully-chosen words on economic and monetary policy will be the issue to watch over the next two days.
The Chinese slowdown is also causing ripples in other G7 markets.
G7 leaders will launch an S.O.S – Save Our Steel Industries.
They are worried about overcapacity – when supply is greater than demand – in China’s steel mills.
Why does this matter?
Because China, the world’s largest steel producer, is accused of flooding other markets with the steel it doesn’t need.
Some EU and US officials say this is ‘dumping’ -when goods are exported at prices lower than they cost to make or prices below those charged domestically.
Western rivals argue China’s actions has pushed down prices and their profits, leading to factories shutting their doors and job losses.
India’s Tata Steel has already put its UK operations up for sale and 2000 jobs have been cut there over the past year. There have also been a series of layoffs in the US industry.
A manufacturing and construction boom, fuelled by a mix of borrowing and government investment, saw China’s steel output expand greatly over the past 25 years.
It produced 803 million tonnes in 2015, according to the World Steel Association, up by 170 percent from 1990 levels.
The same trade body says demand for Chinese steel stood at 672 million tonnes last year. It expects demand to drop further still this year and next.
The United States has already slapped tariffs of 522 percent on Chinese steel, citing Beijing’s alleged refusal to cooperate with anti dumping investigations.
European regulators have imposed provisional tariffs of 16 percent.
But a piece of EU trade legislation, known as the lesser duty rule, means they cannot be raised any further.
The bloc is also divided on what to do next. France wants this rule scrapped. The UK opposes such a move.
China doesn’t have a seat at the G7 but Beijing is making its voice heard.
“Blaming other countries is always an easy, sure-fire way for politicians to whip up a storm over domestic economic woes, but finger-pointing and protectionism are counter-productive,” a commentary from the state-run Xinhua news agency said on April 18th.
“It seems understandable to think of China, the world’s largest steel producer and consumer, as the source of global market woes. Upon closer inspection, however, it’s just a lame and lazy excuse for protectionism,” the editorial said.
Russia might not be at this summit, but its shadow will loom large here.
Japanese Prime Minister Shinzo Abe said in January that he wants Vladimir Putin to be brought in from the cold, arguing that the Russians had a crucial role to play in brokering an end to the conflict in Syria.
G7 foreign ministers in April threw their weight behind the UN-backed peace talks and leaders are expected to reassert their support for “negotiations on political transition away from (President Bashar) Assad’s rule”.
Leaders will once again call on Russia to honour the terms of the Minsk Agreement, which called on Russia to withdraw troops and arms from eastern Ukraine and for local elections to be held there.
Meanwhile, senior EU officials were briefing last week that they want to see other wealthy nations offer more resettlement places for refugees. (Read: help us!)
The EU’s flagship policies to deal with the influx of people onto Europe’s shores both look to be on rocky ground.
Just over 1,600 people from an agreed total of 160,000 have been moved from Greece and Italy under a relocation scheme, while Turkey is threatening to back out of a deal to help stop migrants leaving its territory unless its citizens are granted visa-free travel.
Also look out for British Prime Minister David Cameron trying to win further international support from his G7 counterparts for his campaign to keep Britain inside the European Union.