By Michael Bristow
BBC News, Beijing
A few weeks ago, Chinese and Indian troops held a joint military exercise in which they stormed a mocked-up terrorist training camp.
Mr Singh (R) is paying his first visit to China since he came to power
Soldiers "wiped out terrorists" and "rescued hostages" in what was the first-ever joint military drill between the two sides.
It was immediately hailed as an important step not just for the two armies, but also for two countries that fought a brief war in 1962.
But analysts say there are still a number of major, unresolved issues between the world's two largest developing nations.
These differences mean expectations are low for the first visit to China by Indian Prime Minister Manmohan Singh.
Perhaps the most pressing problem is the territorial disputes. Both neighbours claim the other occupies territory that is rightfully theirs.
One disputed area is the north-eastern Indian state of Arunachal Pradesh.
Special negotiations were begun in 2003 to resolve this and other border issues and, at least publicly, China is upbeat about the progress made.
Speaking at a recent news briefing, Chinese Foreign Ministry spokeswoman Jiang Yu said negotiations were going well.
"We are willing to work together with India so as to reach a fair and reasonable resolution framework," she said.
But Brahma Chellaney, of Indian think-tank the Centre for Policy Research, says resolving the border issue will be difficult.
He says China has hardened its position in recent years.
For example, China has gone back on an agreement that border-related agreements should not disturb settled populations, says the professor of strategic studies.
He also says the Chinese military have made numerous incursions across the border into India over recent months.
Ahead of his visit to China, the Indian prime minister himself said the border issue was "complicated".
There are other problems, too.
India is suspicious of China's military alliances with Pakistan and Burma.
China has its own gripes. It appears none too pleased with the so-called axis of democracy that includes India, Japan, Australia and the United States.
Beijing believes the close co-operation between these four countries could be directed against China.
Tibet is another potential flash-point between India and China.
Chinese and Indian troops have engaged in military co-operation
India continues to give sanctuary to exiled Tibetans in Dharamsala, including the Dalai Lama, a man Beijing continually vilifies as a monk bent on splitting Tibet from the motherland.
"Trade is the only aspect of the relationship that is doing well at the moment," said analyst Mr Chellaney, a statement that is supported by recently-published statistics.
Trade between the two countries has certainly boomed over recent years.
In the first 11 months of last year total two-way trade stood at $34.2bn (£17.4bn), up by more than 50% on the same period in 2006.
But trade between the two is not balanced. China's surplus with India was $9.6bn between January and November of 2007.
There is a growing band of Indian businessmen coming to China to buy manufactured goods.
One, who did not want to be named, said his company buys Chinese equipment that will be shipped back home and used to build steel plants.
"Maybe the technology is available in India, but the delivery time is shorter in China and they have a huge manufacturing capacity," he said.
Despite booming business, Indian External Affairs Minister Pranab Mukherjee earlier this month played down speculation that the prime minister's visit would achieve anything substantial.
"If you are expecting... any dramatic turnaround on certain issues, which are long-pending, it would perhaps be too much," he is reported to have said.
In the short term, India and China seemed destined to make some progress in certain areas and little progress in others.
As another Indian analyst put it, the relationship between the two countries is about mutual concerns, mutual suspicions and mutual goodwill.