When an NBC Olympics analyst irritated South Koreans by crediting Japan for helping the country step toward the future, he waded into an intricate web of friendship, unease and outright enmity among Northeast Asia’s four nations — the two Koreas, Japan and China — and the United States.

The political relationships in this patch of Asia are complex and fraught with the weight of history — and the blood of hundreds of thousands. That history defines this part of the world.

And given that these Pyeongchang Games are followed by Summer 2020 in Japan and Winter 2022 in China, they define the Olympics, too, for the next four years.

We asked The Associated Press’ experts — the people who cover these countries day after day — to prepare a background briefing of the percolating politics in this region where the Olympics are unfolding.

NORTH KOREA AND SOUTH KOREA

South Korea has been threatened, mined, shelled, attacked with commandos and submarines and generally trolled by North Korean propaganda mavens almost continuously since the Korean Peninsula was forcibly divided at the end of World War II into a Soviet-backed North and U.S.-backed South. To say the relationship is complicated is an understatement.

Throughout this drama, South Koreans have learned to live with Pyongyang and, with some exceptions — war and naval skirmishes, for example — taken it in stride. This past year, however, has seen an extraordinary standoff between a belligerent Kim Jong Un testing nukes and missiles in the North and Donald Trump threatening “fire and fury” in Washington, with Seoul in the middle.

Now, during these Olympic Games, Kim Jong Un’s sister flew south with an invitation to talk. What happens next may determine if skepticism is replaced by that strangest of political emotions in the southern part of the peninsula — hope.

NORTH KOREA AND THE UNITED STATES

In a very real way, North Korea owes its existence to the United States, which in an effort to keep the Soviet Union from putting all of the Korean Peninsula under its sphere of influence after Japan’s surrender in 1945 came up with the idea of dividing North and South along the 38th parallel. Of course, it wasn’t long before North Korea’s founder, Kim Il Sung, sent his troops across that line, touching off the 1950-53 Korean War.

The U.S. and North Korea have technically been at war ever since.

To many Americans, that might come as a surprise. The bloody conflict itself is sometimes called the “Forgotten War” and the fact that a peace treaty has yet to be signed is hardly the focus of U.S. public concern. But in North Korea, the war is both a trauma that older people vividly recall and a political rallying tool second only to the Kim regime’s unrelenting vilification of the Japanese, their former colonial rulers.

The standoff hasn’t cooled despite the end of the Cold War and the collapse of the Soviet Union and Pyongyang’s former socialist comrades. But the nature of the confrontation has changed now that Kim Jong Un, Kim Il Sung’s grandson, has developed nuclear weapons and missiles capable of attacking the United States.

JAPAN AND THE KOREAS

In a region where just about every relationship is fraught, this one still stands out.

Despite the fact that a lot of Japanese culture made its way to the islands from China via the Korean Peninsula, Japan has a long history of treating Korea as if it were either somehow inferior or destined to be a Japanese colony — which it actually was from 1910-45. For its samurai-era invasions and those decades of colonialism, the Japanese are to this day the favorite villain in North Korean movies. Their embassy in Seoul is subjected to near daily protests, mostly over Tokyo’s sexual exploitation of Korean women during World War II.

The NBC gaffe hit such a sore nerve not because it was completely wrong — the colonial years did bring improvements, particularly in infrastructure — but because it completely missed the point. Whatever collateral good came out of it, the decades of Japanese oppression were brutal and explicitly designed to subjugate the Korean nation.

That said, it’s a small neighborhood.

Today, Japan and South Korea have crucial economic ties and share tremendous cultural similarities. The cultural chauvinism hasn’t gone away, but mainstream Japanese attitudes toward Koreans have softened. South Korean youth culture — its K-pop and television dramas — are big hits with Japanese women. The resentment and simmering animosity among South Koreans toward the Japanese still runs much deeper, but with time is losing some of its edge.

North Korea, however, is a different story. Part of it is the history, and part of it is the politics of dealing with an openly hostile, totalitarian regime. But hatred and mutual distrust remain the rule.

CHINA AND NORTH KOREA

China has a complex relationship with the two Koreas but a clear overriding goal of maintaining stability and avoiding conflict on its northeastern border. China fought on the North’s behalf during the 1950-53 Korean War and has long been its chief diplomatic ally and top trading partner.

Yet relations have soured since the rise to power of North Korea’s young leader Kim Jong Un, who has defied Beijing’s calls to end his country’s nuclear weapons program. China in response has signed on to increasingly harsh United Nations sanctions targeting North Korea’s foreign trade.

Beijing remains committed to avoiding a collapse of Kim’s regime. For China, that could bring chaos, refugees and potentially U.S. troops to its border.

CHINA AND SOUTH KOREA

They fought each other during the 1950-53 Korean War, but South Korea and China have since developed an active relationship rooted in flourishing trade and investment and Seoul’s continuing efforts to seek help confronting Pyongyang’s nuclear push. Experts believe China wants good ties with South Korea in part to check U.S. influence in the Asia region.

A lot of the countries’ current friction centers on China’s role as North Korea’s last remaining major ally. Beijing dislikes the U.S. military presence in South Korea, and called South Korea’s installation of a high-tech U.S. anti-missile system meant to counter North Korea a security threat.

CHINA AND JAPAN

The relationship between China and Japan is one of close economic ties shadowed by enduring political tensions dating to Japan’s brutal World War II invasion and occupation of parts of China. Relations sunk to their lowest level in years following Japan’s 2012 move to nationalize East China Sea islands claimed by China, setting off anti-Japanese riots in China.

Yet Japanese businesses from automakers to department stores are thriving in China, while Chinese visitors flock to Japan for tourism and shopping. Political relations began to recover in 2014 when Japanese Prime Minister Shinzo Abe met with Chinese President Xi Jinping in Beijing.

Still, the relationship remains fluid, and it’s not uncommon for China to whip up anti-Japanese sentiment when it suits Beijing’s political purposes.

SOUTH KOREA AND THE UNITED STATES

The United States is South Korea’s most important security ally. They fought together during the 1950-53 Korean War while China backed North Korea. The war killed about 37,000 American troops, and the United States still deploys about 28,500 soldiers in South Korea to deter potential aggression from the North.

America’s cultural influence and its big military presence in the country have produced strong anti-U.S. sentiments among some South Koreans who want more equal footing in relations with Washington. China’s rise in recent years has led many in South Korea to believe that since Beijing may one day replace Washington as the world’s sole superpower, it’s time to build more links with China.

Both Seoul and Washington worry about North Korea’s nuclear threat. But there’s long been division in the South on how to resolve that. If the South pushes to expand ties beyond the Olympics without a North Korean promise of disarmament, it could complicate Seoul’s relations with the Trump administration.

JAPAN AND THE UNITED STATES

They were the worst of enemies. Now they’re the staunchest of allies.

Japan and the U.S. have deep military and economic ties that have been a source of friction at times but largely bound them closely together in the post-World War II era. The U.S. has 50,000 troops stationed in Japan and is treaty-bound to defend it in case of attack. It’s a symbiotic relationship that allows the U.S. to maintain a major presence in the Pacific, including an aircraft carrier south of Tokyo at the home port of the Navy’s 7th Fleet.

Japan worries that the U.S. commitment to the region could waver in coming years, and Prime Minister Shinzo Abe has cultivated close ties with President Donald Trump both on and off the golf course to try to prevent that. Japanese companies are major investors in the United States, from their own auto manufacturing plants to SoftBank’s majority stake in wireless provider Sprint.

CHINA AND THE UNITED STATES

The two countries had no relations whatsoever from 1949, when Mao Zedong’s communists took power, to 1979, when Jimmy Carter and Deng Xiaoping established diplomatic ties that have endured through good times and tension ever since.

The relationship is usually cordial, but the long game is one of unease: China has long believed the United States is trying to contain it, and Washington views Beijing’s economic heft and increasing presence on the world stage as a strategic and economic threat. The United States has long criticized China’s human-rights record, and usually meets with outrage from its government for doing so.

Beijing is seen as benefiting from U.S. President Donald Trump’s withdrawal from the Trans-Pacific Partnership. Washington has continued to push China to get tough on North Korea and continues to oppose China’s militarization of islands in the South China Sea.