Churchill, Roosevelt and Stalin carved up Europe at Yalta. Reagan and Gorbachev almost gave up their nukes at Reykjavik. Some summits make history. The personal chemistry between leaders can produce extraordinary and unpredictable outcomes. They also produce great pictures: the walks in the woods and the fireside chats.
As for the clothes, who can forget George Bush's leather jacket, Tony Blair's fingers jabbed inside his excessively tight jeans or Vladimir Putin's reflector shades?
The problem, however, is that most of the time these meetings promise far more than they deliver – though what they invariably achieve is a temporary injection of gravitas for prime ministers and presidents. It is no surprise that Blair allowed hubris to get the better of him. As he later admitted, who wouldn't prefer global grandstanding to the turgid work of public-service reform?
David Cameron has fallen into the same trap, seeing travel-schmoozing as an escape from the drudgery back home. For a Eurosceptic, he seemed curiously to enjoy his get-togethers with Nicolas Sarkozy.
Inevitably, the Brits gravitate towards the Americans. They might start out pledging a more sober relationship, but they can't seem to help themselves. So Dave and Barack bond by cooking burgers on the Downing Street lawn. Next minute, they're being blokey at Camp David.
The journalists covering these events play along with the hype. Thus in one Sunday paper, we had the headline: "Cameron and Obama lead charge to save the eurozone". The only problem is that neither country is in the eurozone and, beyond exhortations, has no clout with the European Central Bank.
Perhaps the reporters don't travel enough to give them a sense of proportion. In their keenness to inject "colour", they produce lines such as: "Mr Cameron and Mr Obama started the day in the Camp David gym, discussing the global economy as they ran side-by-side."
These meetings can be important. Face time is valuable. But there is nothing magical about them. If summits focused on the substance, rather than the style, world leaders might actually get more done. But that would be to deprive journalists of their photo opportunities and politicians their moments in the sun.