They used to be called economic summits, now the agenda is much wider - it covers whatever bothers the leaders that they can agree to talk about.
While the leaders talk, protesters will be kept away
Economics is bound to be discussed and there are some global problems that must be nagging at certain minds at least.
Two issues stand out: deflation and the dollar.
The dollar has sunk to an all time low against the euro or, to put it the other way around, the euro has never been higher.
It is perhaps a potent virility symbol for any euro-lovers who were worried about its decline after the 1999 launch of the European single currency.
But, far more importantly, it is a millstone for European exporters.
Room to cut rates
Germany is in recession: it is a big international trader with, proportionately, a larger manufacturing sector than the other rich countries in the G8.
Manufacturers are especially sensitive to exchange rate changes: a rising euro is the last thing German industry needs.
Inflation is already very low in Germany, and subdued in the other member countries: a further fall could yet bring deflation
There are compensations: it gives the European Central Bank more room to cut interest rates, something German business wants it to do anyway, and, with oil priced in dollars, it is now falling in price in Euro terms.
Even so, the sluggish large economies of the Euro area - Germany, France and Italy - could do without the currency's new strength.
The problem for them is that it probably suits the United States rather well to have a lower dollar.
For sure, the US administration repeats the mantra of its predecessor that a strong dollar is good for America.
But the Treasury Secretary John Snow has also noted that a lower dollar makes it easier to export because it makes American goods more competitive.
In time it might just bring the massive deficit in US trade with the rest of the world under control.
The more expensive imports in the US are also handy for another reason.
When prices are falling, a nice bout of inflation is precisely the medicine that Dr Greenspan at the Federal Reserve would be ordering
Inflation is very low in the US and some economists are clearly concerned about the possibility of deflation or falling prices.
That is not just falling prices for some goods, but a fall in the overall price level.
It is a pernicious problem, and not a theoretical or a remote historical one.
It has plagued one G8 country, Japan, for the last decade: it is a central element in the country's persistent economic stagnation.
Within the G8, Japan is the only sufferer so far.
But inflation is already very low in Germany, and subdued in the other member countries: a further fall could yet bring deflation.
Danger for Germany
A recent study by the International Monetary Fund found no evidence to support strong concerns about generalised global deflation.
Even so there was some risk and in some countries, notably Germany, the risks are significant.
Deflation is so pernicious because it makes debts more burdensome: personal incomes and profits may fall but debts do not and so they become harder to repay.
What can the G8 do? Well, the dollar's decline helps the US to reduce the risk while deepening the danger for Germany.
The interest rate cuts already made in G8 countries also help.
And so might the tax cuts that the US Congress has agreed.
No sign of panic
If that does not work there are what central bankers have been calling unorthodox measures.
That covers a range of options, some of them amounting to measures to push up the amount of money in circulation - the kind of thing that used to be decried as irresponsible and a cause of inflation.
When prices are falling, a nice bout of inflation is precisely the medicine that Dr Greenspan at the Federal Reserve would be ordering.
But do not expect cries of panic and a programme of concerted anti-deflationary action from the summit.
For one thing, they do not want to frighten the horses - that is you, me and the financial markets.
And they do not think it is all that likely to happen.
But the chances are they are a little nervous and will promise one another to be vigilant.
Let's hope they are.