Now the US and China face the nitty-gritty
The pleasantries have been exchanged, now the real challenges will begin.
The Chinese and American leaders were on their best behaviour during President Hu Jintao's state visit to the US last week.
They put relations back on a cordial footing after a year of disputes in areas from trade and currency policy to military and regional security.
But American analysts said that while China was pleased with the joint statement incorporating the term 'co-operative partnership', the US was more reserved and would continue to judge China's sincerity through its actions. Jobs and the economy were Barack Obama's top concerns, but it was issues such as North Korea and human rights that would really test the relationship in the long run, they said.
Arms sales to Taiwan will be China's key test for the US.
On the North Korea issue, reports have emerged that Obama put pressure on Hu during their private dinner, saying the US might station more troops in South Korea if China did not work harder to rein in its fellow communists in Pyongyang.
'The US keeps telling China over and over again that this time is not the same as before,' said expert on Asian security Douglas Paal, from the Carnegie Endowment for International Peace. 'North Korea now has missiles, and nuclear weapons that threaten us. No US president can fail to take action.'
Some progress has been seen on the Korean Peninsula since the summit. North Korea has proposed - and South Korea has agreed to - high-level exchanges that might result in a meeting of defence chiefs.
In the joint statement issued after the Hu-Obama summit, China for the first time echoed US concerns about North Korea's uranium enrichment programme, revealed in November during a visit to Pyongyang by a US scientist.
Paal said the strategic interests of China and North Korea were not aligned. China wanted a quiet Korean Peninsula, he said, while North Korea was seeking attention from the US, South Korea and other powers by stirring up trouble.
This made it difficult to tell how long Pyongyang would stick to any set course of action and meant China needed to push North Korea harder on ending its nuclear ambitions.
'It has to take a risk on short-term stability,' Paal said. 'It will gain a more stable neighbour, with no nuclear power, in the long term.'
Arms sales to Taiwan, on the other hand, were described by Paal as a problem of 'one choice and three compulsions'.
If China decided to increase military pressure on Taiwan, as it was doing now with a continued build-up of missiles, aircraft and other offensive capabilities opposite Taiwan, then Taiwan's leader would be compelled to seek arms from the US.
The US would be compelled to sell them for political and legal reasons and China would be compelled to criticise such sales.
'This is a vicious circle, and the place to fix it is at the choice,' Paal said. Military expert Dr Michael Swaine, also of the Carnegie Endowment, said there was another potential problem, given China's continued development of its overall military capability.
Despite improved political relations and closer economic ties between China and Taiwan, Swaine said 'you don't have the development of serious confidence-building measures that could really result in the reduction of military deployments across the Taiwan Strait'.
He said: 'The Chinese have made some reassuring comments on this, but haven't indicated they are prepared to unilaterally reduce military deployment as a goodwill gesture to start the ball rolling.'
'They tend to think [such a reduction] should be a response to some kind of political dialogue on reunification with Taiwan.'
In the absence of such reductions, US arms sales were likely to continue, further upsetting China.
'The US should consider the possibility of developing a way of engaging more directly with the Chinese on some kind of mutual understanding about restraints,' Swaine said. 'The Chinese would restrain deployment or development of classes or types of weapons of relevance to Taiwan.
'And the US would, as a result of that, restrain itself from or put a moratorium on arms sales.
'This hasn't happened because the US has pledged ... not to speak directly to China about its arms sales ... but I'm not sure if the US' hands-off approach will be sufficient to maintain stability across the Taiwan Strait given the change in dynamics.'
Another challenge was China's growing naval reach in the western Pacific, with strategic fault lines opening up between China and the US in the East China and South China seas last year. 'The US tends to believe that stability in the western Pacific rests to a certain extent on US maritime predominance ... and China does not entirely accept that argument,' Swaine said.
Frank talks on the operations, deployments and purposes of the two militaries were necessary, he said, and contacts could start with co-operation in less sensitive, non-traditional security areas like fighting terrorism and piracy, as agreed during US Defence Secretary Dr Robert Gates' trip to Beijing this month.
'This is a subtle and complex problem, not one of China putting together a military and preparing to deploy force against somebody. It has a lot to do with strategic balance and perceptions of security, or insecurity, [in the region] and leverage over these issues,' Swaine said.
Professor David Lampton, of John Hopkins University, said Obama could be expected to take a firmer stance on human rights and Tibet , after repeatedly mentioning the need to respect universal human rights during his summit meeting with Hu. 'During Obama's first year, there was a perception that the president was not staunch enough on some of the traditional positions of the United States,' Lampton said.
'I think what you are seeing now, particularly in light of a Republican House, is the president trying to re-establish his leading role in foreign policy. He talked about the one-China policy, but he also talked about human rights.'
Veteran China law professor Jerome Cohen said human rights would be the acid test for Sino-US relations as 'the one area of contention where China's leaders have shown no willingness to yield to American pressure'.
'From today's vantage point, one can see little accomplishment in the human rights field despite the Obama administration's efforts to give the issue more prominence. The proof will emerge in the next few months as we witness whether there is any relaxation of repression in China, whether detained and disappeared human rights victims are released, and so on,' he said.
The US Congress pressed Hu hard on human rights issues when he was in Washington and such ideological differences will make deepening friendship difficult.
In Obama's State of the Union Address on Wednesday he made a subtle comparison of the governance systems in China and the US, saying that while Americans argue about everything 'some countries don't have this problem. If the central government wants a railroad, they build a railroad, no matter how many homes get bulldozed. If they don't want a bad story in the newspaper, it doesn't get written'.
Professor June Teufel Dreyer, of Miami University, said that going forward, a major problem for Sino-US relations would be domestic sentiments, which would make it difficult for the two countries to change their stance on issues such as North Korea and trade.
'So the best we can hope for is what we've just had,' she said.
'There's a nice ceremony, and the two sides issued a joint statement which is mostly void of any concrete meaning ... Perhaps you could call this a soothing exercise by each side for its own domestic consumption.'
But many US experts lauded the joint statement's commitment to high-level exchanges. US Vice-President Joseph Biden will visit China this year and Vice-President Xi Jinping will make a trip to the US.
'It is very important for US and Chinese leaders to trust each other,' Lampton said. 'The earlier that process begins the better.'