Here are key topics that the uneasy neighbours will find difficult to solve:
India has repeatedly demanded greater access to China’s markets in recent years and pressure has grown because of the rising trade deficit of about US$55 billion in Beijing’s favour. India’s pharmaceutical and software industries have in particular lobbied for a more open border.
India wants trade dealt directly with China, but their talks will have an impact on the free-trade accord that Southeast Asia’s ASEAN is negotiating with major partners including Beijing and New Delhi.
Many in India see China’s trade war with the United States and international scrutiny of its commercial practices as a window to raise trade concerns.
India is one of the key countries where Chinese telecoms giant Huawei wants to establish its next-generation 5G technology.
Xi is expected to press Modi to give Huawei the green light to take part in 5G trials, in the face of US opposition due to security concerns over Chinese-made equipment.
Huawei is already a major player in India’s smartphone market but the government has yet to make clear its stance on the company’s role in Indian 5G networks.
Many Indian security analysts have raised concerns over allowing Chinese firms into strategically sensitive areas. But India’s Foreign Minister Subrahmanyam Jaishankar last week denied that Huawei was a “political problem”.
India-China tensions rose again after New Delhi’s move on Aug 5 to revoke the autonomy of Jammu and Kashmir, a Muslim-majority Himalayan region also claimed by Pakistan. China controls a part of Kashmir, which is in turn claimed by India. China’s criticism of India’s constitutional move angered the Modi government.
The rivals have a long-pending border dispute in Ladakh – a strategic Buddhist-dominated region within Kashmir that is to be split into a separate Indian administrative territory under the changes.
Both armies frequently cross into territory held by the other side around Ladakh, which has China’s restive Xinjiang to its north and Tibet to the east.
India has been a vocal critic of China’s Belt and Road global infrastructure programme that includes a key project through Pakistan-administered Kashmir.
Besides Ladakh, India and China also have a decades-old dispute over Arunachal Pradesh, an Indian state bordering Tibet.
They went to war over the territory in 1962 and China still claims about 90,000 sq km of land under New Delhi’s control. The Buddhist and Hindu dominated region with dense forests and waterfalls is also home to many indigenous tribal communities.
In 2017, the neighbours had a high-altitude standoff in Bhutan’s Doklam region after the Indian army sent troops to stop China constructing a road there. Doklam is part of a long-pending border tussle between China and tiny Bhutan, which counts India as one of its closest allies.
Modi and Xi’s last summit in Wuhan two years ago helped end the showdown, but Doklam remains tense. India has held two significant military exercises close to its disputed borders with China in recent weeks.
DIPLOMATIC DAGGERS DRAWN
The two Asian giants are also competing for influence across South Asia. Xi is due in Nepal on Sunday after these talks and their strategic rivalry can also be seen in projects and diplomatic pushes in Sri Lanka, Afghanistan, Myanmar and even the Maldives.
The two leaders discussed greater regional cooperation at their last summit but experts say little has changed since. India’s worries about Chinese initiatives such as the Belt and Road project have bolstered its support for the Quad security dialogue with Japan, the United States and Australia that has been pushed as a democratic counter to China’s more assertive stance. India participated in its first ministerial-level meeting in New York last month.