By Gabriel Gatehouse
BBC News, Sochi
This was George W Bush's and Vladimir Putin's last meeting as leaders of the two great former Cold War adversaries, and they looked like the best of friends.
The two presidents were on first name terms throughout their news conference. George Bush remarked that their meetings had always been agreeable, even when they disagreed.
Mr Putin and Mr Bush seem at ease together
But disagree they do, and on the most fundamental issues - Nato expansion and missile defence.
On the latter, Vladimir Putin emphasised that his country's opposition to American plans for a missile defence shield in Eastern Europe went deeper than simple objections of protocol.
"This is not about language, this is not about diplomatic phrasing or wording, this is about the substance of the issue," he said. "I'd like to be very clear on this. Our fundamental attitude to the American plans has not changed."
The first time they met, George Bush announced he had caught a glimpse of Vladimir Putin's soul. Apparently, he liked what he saw.
"I looked the man in the eye," he said in 2001. "I found him to be very straightforward and trustworthy... I wouldn't have invited him to my ranch if I didn't trust him."
Seven years on, that personal chemistry still seemed to be intact. On the doorstep of his dacha on Saturday, Vladimir Putin greeted the First Couple of the United States with a hug for Mr Bush and a pink bouquet for his wife.
The two presidents took an evening stroll along the southern Russian coast. And, as the sun sank into the Black Sea, they will have had time to reflect on a personal relationship that is soon to come to an end.
Mr Bush seemed almost sad at their imminent parting.
"It won't be our last meeting as people, it's our last meeting as presidents of our country. And it's a little bit nostalgic," he said after their meeting today.
But while the two men do seem genuinely to like each other, the feeling of trust is not mutual. In Sochi, President Bush yet again gave his assurance that the proposed American missile shield was not aimed at Russia.
The trouble is, Vladimir Putin simply does not seem to believe him. As with the issue of Nato expansion, Mr Putin sees the US plan as an attempt to contain Russia.
At last week's Nato summit in Bucharest, Russia scored a partial victory on the question of expanding the alliance. Nato did not invite Ukraine and Georgia, both former Soviet states, onto its Membership Action Plan.
But this is only a temporary reprieve for the Russian president. Talks will begin again in December, and sooner or later, Nato has said, they will become full members.
On the question of missile defence, President Bush got the backing from his Nato allies, and so he can go ahead anyway.
But it is a measure of how seriously the United States now takes Russia as a player on the world stage that they are still talking and still searching for compromises.
The two leaders will have had time to reflect on their relationship
And it appears that Mr Putin appreciates the effort.
"The Americans have listened to our concerns," he said on Sunday. "We feel that the president of the United States is serious about this and genuinely wants to solve this problem."
In its coverage of their first meeting those seven years ago the BBC News website reported: "The two men still differ over enlarging Nato and US missile defence plans, but they exchanged warm words."
Those exact same words could apply to their last meeting today. So has nothing changed?
Many of the issues that divided Russia and the US in 2001 continue to do so today. Under Mr Putin though, Russia has become richer, and more assertive on the world stage. And Mr Bush has had to take account of that.
But when the new presidents of Russia and the United States come to have their first meeting some time next year, they will still be discussing the thorny questions of Nato expansion and missile defence.