Joe Biden wants to restore American credibility and rally the democratic world to a historic struggle with authoritarians led by Russia and China.
Boris Johnson wants to fly the flag for the UK – and needs to cement global relationships to vindicate his post-Brexit vision of “global Britain.”
Others are preoccupied with Covid 19, the ever-present challenge of a global response to climate change, and the coming shock of the post-pandemic recession.
But everyone has their own national interests to defend at the G7 summit, and they are not always comfortably aligned.
Here is what the seven nations want.
The G7 is the first test of the grandiose, if somewhat vague, ideas of a "Global Britain" Boris Johnson’s government set out in the Integrated Review of foreign policy and defence published in spring.
The central thesis is that post-Brexit Britain can be a “convener” – a country with the diplomatic clout and respect of allies and adversaries alike to broker progress on the enormous global challenges facing all governments.
Two global issues stand out.
The most pressing is Covid-19 recovery. Mr Johnson has set a date of getting the entire world vaccinated by the end of 2022.
There are strong doubts about whether that is achievable, and major differences over the details – especially whether rich countries should waive intellectual property rights on vaccines. But he will be able to claim a victory if the G7 produces some kind of action pan.
UK Prime Minister Boris Johnson talks with primary school children in Cornwall ahead of the G7 summit
The other big one is climate change. The UK is hosting the COP 26 summit in Glasgow in autumn, and Mr Johnson will be keen to use the G7 to lay the ground-work for a successful global agreement to reduce emissions and arrest temperature rises.
He will be in alignment with Mr Biden on China and Russia.
Then there are domestic British interests. The clash with Europe over trade and the Northern Ireland protocol will dominate meetings with all European leaders, and indeed Joe Biden.
And, of course, trade. The guest list – South Korea, South Africa, Australia and India – reflects British desire for free trade deals beyond Europe.
G7 Summit agenda
Emmanuel Macron is embattled at home, and a rising far-Right means he will face a tough election in 2022.
So he will want to be seen to be vigorously defending French interests at the G7, and demonstrating that Paris remains at the centre of global leadership.
He will be very happy to push Mr Johnson on contentious Brexit issues, including the rights of French Fishermen and the future of the Northern Ireland protocol.
And he will be pushing hard for more Covid assistance for Africa, and eager to claim the credit for any that emerges – it is a traditional sphere of French leadership that Mr Macron has no intention of relinquishing to any of his fellow Western leaders.
He has come out unambiguously in favour of Mr Biden’s call for a vaccine patent waiver, aligning himself with the United States, South Africa, and India, but putting himself on a collision course with EU ally Angela Merkel and the UK’s Boris Johnson.
G7 venue and hotel map
This summit will be Angela Merkel’s last before she steps down as Chancellor in September.
After 15 years in power, she is by far the most experienced of the leaders present, and carries vast credibility as the stateswoman who held the liberal world order together during the turbulent Donald Trump years.
She will be unveiling an ambitious German plan on climate change to achieve net zero by 2045, and she will push Mr Johnson hard over the Northern Ireland protocol.
Her meetings with Mr Biden may be strained. She has refused to cancel the Nord Stream 2 gas pipeline between Germany and Russia – which the US believes is a Kremlin foreign policy tool designed to weaken Europe and undermine solidarity with Ukraine. She also opposes his idea of waiving Covid vaccine patents.
Yoshihide Suga, the Japanese Prime minister, has been in office for less than a year.
He will also be looking for backing for his not entirely popular decision to push ahead with the Tokyo Olympics this summer, despite the Covid pandemic.
He will also want reassurances from allies over China, especially its increasingly assertive claims to waters in the Western Pacific, but may resist anything he considers excessively confrontational rhetoric about Japan’s superpower neighbour.
Japan's Prime Minister Yoshihide Suga speaks to reporters before leaving for the G7 meeting in Britain
Slightly irritating to Japan will be the presence of South Korea as a guest. The two neighbours, although both US allies with deep concerns about China, have strained relations over 20th century history.
And Japan was alarmed by suggestions in the run-up to the summit that Mr Johnson wanted to recruit the guest powers to a new, semi-formal “D-10” group of democracies to counter China. That idea, could dilute the clout of the G7 and jeopardise Japan’s status as the only Asian member at the top table.
Justin Trudeau will be looking to repair ties with the US following frequent disagreements with Mr Trump between 2016 and 2020.
He will be well aligned with Mr Johnson and Mr Biden on China, which is holding two Canadians on spying charges in retaliation for Ottawa’s arrest of Huawei executive.
Prime Minister Justin Trudeau waves as he boards a government plane in Ottawa to head to the G7 summit in the UK
Credit: Adrian Wyld /AP
He has been less enthusiastic about Mr Biden’s call for a Covid vaccine waiver, but has indicated he would not block one – provided it was negotiated via the World Trade Organisation.
But he may be slightly embarrassed when discussions turn to climate change.
Canada is the world’s fourth largest oil producer and has the highest rate of emissions growth of any G7 nation since the Paris Climate Agreement was signed in 2016. Critics say expansion of the hydrocarbons industry contradicts Mr Trudeau’s commitment to reduce emissions.
Italy’s prime minister Mario Draghi was previously a governor of the European central bank, and his G7 shopping list is appropriately focused on economics.
He is a big backer of the proposed global minimum 15 percent tax on multinationals, which G7 finance ministers are close to agreeing. He also wants mechanisms to stop poorer countries falling into debt as the global pandemic gives way to a global recession.
In talks with Mr Biden and European leaders he will raise concerns about migration across the Mediterranean – and in particular instability in Libya, Italy’s southern neighbour.
The United States
Mr Biden probably has the biggest performance anxiety of all.
He has already said he wants to prove America is “back” as a global leaders, and he has set himself ambitious goals.
He wants other leaders to agree to waiving patents on Covid vaccines – a demand put forward by India and South Africa, who will be attending the summit as guests, but resisted by Mrs Merkel and the UK’s Boris Johnson… at least for now.
He wants commitments to help developing countries improve infrastructure and pivot to a green economy, in direct competition with China’s belt and road programme.
US President Joe Biden waves on his arrival on Air Force One at Cornwall Airport Newquay for the 2021 G7 summit
Credit: Pool Reuters
And perhaps most boldly of all, he wants to rally democracies for what he sees as an epochal global struggle between open societies and their enemies – personified by China and Russia.
In exchange for ruling out sanctions on Nord Stream 2, he will want commitments from Mrs Merkel to back Ukraine and be serious about standing up to Russia.
He will have stern words with Boris Johnson and the European leaders over the Northern Ireland protocol. The US will not tolerate anything that jeopardises the Good Friday Agreement. on Thursday that they must "behave" in order to attract jobs and investment.