Equally intractable are two conflicts in East Asia that originated in the Cold War. China views Taiwan as an indissoluble part of its territory. Then there is North Korea, an isolated and unpredictable nuclear weapons state.
East Asia today has been compared with Europe in 1914, with North Korea viewed as the most likely potential trigger for an outbreak of major armed conflict.
The South China Sea
In the South China Sea, there are five countries at loggerheads over their maritime borders: China, Brunei, Malaysia, the Philippines and Vietnam. Also at stake is control over fisheries and oil and gas fields.
The Paracel Islands are disputed by China, Taiwan and Vietnam. The Spratly Islands are disputed by China, Taiwan, Malaysia, the Philippines, Vietnam, and Brunei.
China is reportedly building artificial islands in the region, which some fear could be used for military purposes. China and its Southeast Asian neighbours have agreed a code of conduct to try and avoid flashpoints, but observers worry that it is not up to the task.
The East China Sea
Eight uninhabited islands and rocks in the East China Sea have been the subject of long-standing rival claims to sovereignty on the part of China, Japan and Taiwan. They are called the Senkaku Islands in Japan, the Diaoyu Islands in China and the Tiaoyutai Islands in Taiwan.
Japan and China have also been unable to agree a maritime boundary in the East China Sea. As in the South China Sea, competition over oil and gas resources is a big factor.
In late 2014, both parties agreed to establish a 'maritime crisis mechanism' to help defuse rising tensions. But this mechanism is fragile and untested.
There is a risk of escalating tension between China and Taiwan over the next few years. An opposition party sympathetic to the idea of an independent Taiwan could win presidential elections scheduled for January 2016 in Taiwan.
With just under two million soldiers on the ground, the Korean peninsula has the greatest concentration of armed forces anywhere in the world. North Korea has nuclear warheads but (according to most experts) not yet the missiles to deliver them reliably. South Korea is rapidly modernising its armed forces and becoming less reliant on American support.
The US role
The US has undertaken a 'pivot to Asia' since 2011. By 2020 it plans to base 60% of its navy and air force in the Asia-Pacific region. It has treaty obligations to come to the aid of Taiwan, Japan and South Korea if any of them is attacked. China opposes the US pivot but does not want open conflict. Many other countries in the region strongly favour the pivot.
Although it has criticised China for acting aggressively, the US takes no position on the territorial and maritime disputes in the South and East China Seas. It calls on all sides to seek a resolution of issues through peaceful dialogue and consistent with international law.
While the UK, like the US, does not take a position on the sovereignty disputes in the South and East China Seas, in early 2015 the previous Government indicated that the UK has "an important stake in Asian security" and that, under the 1971 Five Powers Defence Arrangements, a series of bilateral agreements whose signatories are the UK, Australia, New Zealand, Malaysia and Singapore, it is "ready and able to mobilise in support of Asia Pacific allies, friends and partners".
Major shipping lanes vital to the regional and world economy are located in the East and South China Seas. It is estimated that every year the South China Sea facilitates the movement of over half of the world's oil tanker traffic and over half of its merchant vessels by tonnage. The Malacca Strait between Singapore and Indonesia is a particularly vulnerable 'chokepoint' for sea-borne trade.
Over the last decade, the UK has sought to boost trade in goods and services with East and Southeast Asia. Since 2010, UK trade has risen most rapidly with China and South Korea. In 2013, China, Japan and South Korea accounted for 6.6% of total UK imports and 9.1% of total exports.
Dates to look out for
- November 2015: Association of Southeast Asian Nations (ASEAN) Summit
- November 2015: Asia-Pacific Economic Cooperation (APEC) Leaders' Meeting
- January 2016: Taiwan elections