This year's G8 summit will unfortunately be remembered for the death of a demonstrator shot by police, and two days of the kind of violent protests which have come to mark international meetings of this kind.
The leaders of seven major industrialised countries, plus Russia, met behind steel barricades that sealed off a large area of the old centre around the port.
The unprecedented security reinforced the image of powerful politicians cut off from their own people and the world.
At the end of their meeting, the G8 leaders deplored the violence, loss of life and mindless vandalism.
They defended the right of peaceful protesters to be heard, but said a violent minority could not be allowed to disrupt their discussions.
The British Prime Minister, Tony Blair, responded angrily to the suggestion that the violence meant summits had to change.
It was turning democracy on its head, he said, to conclude that democratically elected leaders should not meet because people came to riot and throw petrol bombs at the police.
Nevertheless, the format of next year's summit in Canada is likely to change.
The Canadian Prime Minister, Jean Chretien, said the scale of the meeting in the western province of Alberta would be reduced, with much smaller delegations.
The Italian Prime Minister, Silvio Berlusconi, said it would be held in a mountain resort in the Rockies, though Mr Chretien would not confirm that.
But this tactic for keeping away violent demonstrators would contradict recent moves to open up the G8 summit to a wide spectrum of civil society.
It might also make the leaders look even more isolated.
This year the G8 leaders went to great lengths to counter the view that they were arrogant rich politicians who did not care about poor countries.
The overall theme was fighting global poverty; as the final communique put it, making globalisation work for everyone, especially the world's poor.
New initiatives were announced. There was a programme to help developing countries develop the use of information technology, an effort to bridge the digital divide.
A plan for Africa set out a partnership between the G8 and a similar number of African countries.
Several African presidents were invited to Genoa to take part in one of the sessions.
The G8 pointed to progress in the number of highly indebted countries qualifying for debt relief - 23 now, compared with only nine a year ago.
The total relief in due course should amount to more than bn dollars. Some of it will be directed into basic education and health.
The summit also saw the formal launch of a global fund to fight Aids, malaria and tuberculosis. Promised contributions so far are a little more than bn dollars.
The response from campaigners was that the amount was hopelessly inadequate, chicken feed compared with the scale of modern western government spending.
On debt relief, only unconditional cancellation of all debts would satisfy them.
The big powers also set conditions. Aid depends to a greater or lesser degree on respect for democracy in the recipient country - the rule of law, economic reform and efforts to stamp out corruption.
That has to be borne in mind when this year's host, Mr Berlusconi, says the G8 does not want to govern the world or impose its will on other countries.
It may not literally impose, but it certainly believes it knows the way things should be done.
Global warming was the issue on which the countries of the G8 clearly could not resolve a basic disagreement among themselves.
There was no shift in President Bush's rejection of the Kyoto treaty; no shift in the European Union's determination to ratify it.
The G8 leaders said they would nevertheless work together to stabilise emissions of greenhouse gases; the Americans shared this objective.
Mr Bush said they were serious about it and were working out a strategy to do just that.
The fact remains that the United States will not accept internationally binding limits on gas emissions. That is a gaping hole in international action.
The Genoa summit as such can hardly be blamed for failing to bridge the gap. If the G8 were still an informal gathering of leaders exchanging ideas, the original fireside chat at Rambouillet in 1975, it would not matter.
But the clock cannot easily be wound back. The G8 summits have become huge events laden with unrealistic expectations. Inevitably, these are never met.
Even if the politicians could manage without the publicity, a media black-out would bring charges of secrecy and unaccountable behaviour.
The governments are engaged in messy compromises; while campaigners operate on certainty and passionate conviction.
They are never going to see things the same way.