Now a warm handshake between the two biggest countries in the region naturally leads to the anticipation of more co-operative steps. Stretching the imagination further still, the eventual formation of Asia's answer to the European Union could be on the cards in the future.
For the moment, the partnership between China and India is not only important for the two countries, but also "adds weight to the role of the entire continent," said Zhai Kun, a senior fellow with the China Institute of Contemporary International Relations (CICIR).
But what is Asia's role in the world?
This is exactly the question that political, business and opinion leaders will ponder in the annual conference of the Boao Forum for Asia. The theme of the conference is the New Role of Asia.
"More economic activities are taking place in Asia than in any other area. Growth rates here have outpaced elsewhere. This naturally leads to attention on Asia," said Long Yongtu, secretary-general of the forum.
"We should have an appropriate assessment of what kind and how big a role Asia can play," Long added.
"We should not overstate it, nor should we understate it."
To Zhang Yunling, director of the Chinese Academy of Social Sciences' (CASS) Institute of Asia-Pacific Studies, Asia's new role is two-fold.
It is first and foremost economic.
Economic power
In fact, Asia's rise on the world stage started with the so-called "Asian miracle" - the economic success of Japan and then the small "dragons" and "tigers" such as South Korea, Hong Kong, Singapore and Thailand.
The burst of the economic bubble in Japan and the 1997-98 Asian financial crisis cast a shadow over Asia's success story, but most East Asian economies quickly returned to growth again.
And China's rapid emergence as an economic power on the world stage adds much to East Asia's attractiveness.
Now India, after decades of slow growth, is also catching up.
Both China and India are growing at rates faster than almost all the other major economies in the world in recent years.
The Indian economy is smaller than China's. But given India's size and influence, the emergence of its economic power on the continent is fundamentally changing Asia's position in the world, said CASS' Zhang.
The prospects of a triad of Japan, China and India will make Asia a vital engine for the world economy.
Zhang said the new role of Asia is also that of a more prominent global player in international relations, a player that can be the peer of the European Union and the United States.
Starting from escalating co-operative steps in East Asia, regional co-operation is gaining momentum across the whole continent.
Official dialogue between the 10-member ASEAN (Association of Southeast Asian Nations) and China, Japan and the Republic of Korea was launched in 1997.
The dialogue has progressed well and created a favourable environment for all sorts of regional co-operation.
Now the 10 plus 3 meeting is evolving into a meeting of 13 members, which is scheduled to have its first East Asia Summit in Kuala Lumpur late this year.
The smooth progress has interested some neighbours. Both India and Australia have expressed an interest in joining co-operation in East Asia.
The co-operation in this area is not only about the emergence of a unified regional player, but also about the introduction of the "Asian approach," CICIR's Zhai Kun said.
Although they still have unsettled disputes on issues such as territory and history, they can put them aside while beginning to sit down together to talk about co-operation in other areas.
"Instead of resolving the problems right from the start, they tend to create a favourable atmosphere first then co-operate in certain areas while tackling the real thorny issues step by step," Zhai said.
Despite territorial disputes among China, Viet Nam and the Philippines over South China Sea, they recently agreed to put the disputes aside first and explore natural resources there together.
In terms of development, Asia can also provide experience for developing countries in other continents, such as Africa.
Asian and African leaders gathered this week in Indonesia to talk about ways to face challenges in the era of globalization. Asian countries are generally more successful in developing their economies and can share their experiences with Africa.
"So you see, Asia also has a role in its relation to Africa to play," Zhai said.
Japan's role
Japan's integration with Asia will be an important part in the process of Asia developing its new role.
Japan, now the biggest economy in Asia, is closer to the Western world in terms of politics and economic systems.
The increasing significance of Asia has prompted Japan to start "returning to Asia."
However, as Japan has spent decades becoming a "Western country," it will be a long process for it to become a real Asian country again, said CASS' Zhang.
A key problem for Japan is its attitude towards its history of invading other Asian countries, which makes Asian countries worry about the revival of its militarism. This undermines Asian nations' trust of Japan.
In addition, Japan, after being the sole leading economic engine in Asia for decades, also needs to make adjustments and accept the reality of the emergence of China and India as new economic powers.
The two issues every now and then emerge to strain relations between Japan and others. The latest dispute between Japan and other Asian countries over history textbooks is an example.
However, Japan's often uneasy relationships with other Asian countries are not the only obstacle for Asia in its pursuit of a more prosperous and harmonious community."
One look around will find that there are still lots of problems. In the north, the nuclear issue on the Korean Peninsula has not been solved; in the south, there are a series of places still involved in territorial disputes.
In terms of economic development, all countries in the region, including China, Japan and India, still face a myriad of challenges.
"Asia still has a long way to go," said CICIR's Zhai.
