The relationship between the United States and China is important but delicate. During the 2008 presidential campaign, Barack Obama promised to "press China to end its support for regimes in Sudan, Burma, Iran and Zimbabwe."

We asked several foreign policy experts whether the Obama administration has followed up on this pledge. We'll take each of these four countries in turn.

• Sudan. The administration has "worked hard to change China's policy towards Sudan and had some success in the process," said David Shinn, an adjunct professor of international affairs at George Washington University who served as U.S. ambassador to Ethiopia from 1996 to 1999 and to Burkina Faso from 1987 to 1990.

"China eventually and belatedly was the key player in convincing Khartoum to accept a combined African Union/United Nations peacekeeping force in Darfur," the war-torn region of Sudan, Shinn said. "Under pressure from the U.S. and other countries, China -- contrary to previous policy -- made this happen."

China, he said, also played "a useful role behind the scenes in supporting the Comprehensive Peace Agreement between Sudan and South Sudan," the newly created country that was formerly part of Sudan. China worked with US envoys to help ensure implementation of the peace agreement, Shinn said.

"The U.S. and China still have differences over policy towards Sudan, and the U.S. has not succeeded at every level, but it has tried hard," Shinn said.

• Burma. Obama visited Burma -- sometimes called Myanmar -- shortly after winning reelection in 2012. It was a historic trip to a nation formerly considered an international pariah and it included a visit by Obama to meet opposition leader Aung San Suu Kyi at the home where she was held in house arrest for years.

The visit was widely considered a way for the United States to encourage further reforms initiated by the Burmese government in 2011. "This remarkable journey has just begun, and has much further to go," Obama said. "Reforms launched from the top of society must meet the aspirations of citizens who form its foundation."

David Steinberg, a professor of Asian studies at Georgetown University, said that the U.S. "has not, and will not in my view, confront China in Myanmar. Rather, the Burmese have recognized that a neutralist policy that balances China and the West and (the Association of Southeast Asian Nations) is in their best interests. The U.S. understands this, I think. The changes and progress that have been created in Myanmar -- and they are extensive -- have been done by the Burmese themselves, and not by the U.S."

Alan D. Romberg, director of the East Asia program at the Stimson Center, a foreign-policy think tank, agreed. "The dramatic turnaround in Burma has a lot to do with the U.S., and I suspect it has little to do with China," said. "But China certainly hasn't blocked this development."

• Iran. The U.S.-China relationship as it concerns Iran is the most complicated of the four cited in this promise, largely because the effort to keep Iran from getting a nuclear weapon ranks so high on the United States" foreign-policy agenda.

Historically, China, along with Russia, has been less willing to go along with United Nations measures to punish Iran over its nuclear activities than other key nations. This is believed to stem in part from China's commercial ties to Iran.

"China is the world's second-largest oil importer," wrote Erica Downs and Suzanne Maloney in the March/April 2011 edition of Foreign Affairs. "Iran's oil and natural gas reserves rank among the world's largest, making the country an attractive destination for China's (national oil companies), which are increasingly looking for opportunities abroad."

Yet ties between China and Iran "are hardly ironclad," Downs and Maloney added, because "China does not want to be isolated on major global issues." This observation has been borne out over the past few years as China has sided with the U.S. against Iran on some key votes.

In June 2010, China joined with the U.S., France, Germany, Russia and the United Kingdom in approving a fourth round of U.N. Security Council sanctions against Iran, including an expanded arms embargo and tighter restrictions on financial and shipping enterprises related to "proliferation-sensitive activities." The resolution also spelled out China's willingness, along with the rest of the Security Council, "to further enhance diplomatic efforts to promote dialogue and consultations towards a negotiated solution."

Meanwhile, in September 2012, China joined the same five nations in sponsoring a resolution at the International Atomic Energy Agency's governing board that rebuked Iran for continued intransigence on its uranium enrichment program. The measure passed easily. Later that month, during the meeting of the U.N. General Assembly, Chinese Foreign Minister Yang Jiechi said the dispute over Iran's nuclear program had reached "a new, crucial stage" and called for Iran to reengage in international talks.

• Zimbabwe. Shinn said that U.S. pressure on China has been less effective in Zimbabwe, where long-serving dictator Robert Mugabe has pursued anti-democratic policies and sometimes violent expropriations of land, drawing sanctions from the West that have left the economy in freefall.

China's Communist government has ties to Mugabe dating back to his days as an anti-imperialist leader. "China was been linked to Robert Mugabe since he was the leader of the liberation movement that won independence," Shinn said. "China tends to stick by its friends. Once Mugabe dies or is forced out of office, China will probably be more receptive to policy change. The U.S. has tried, but there is not much to show for it."

Putting it all together, U.S. diplomacy with China seems to have paid dividends in relation to Sudan and, to a certain extent, Iran. Meanwhile, China hasn't objected to U.S. efforts in Burma, but engagement with the Chinese hasn't accomplished much yet in Zimbabwe. On balance, we rate this a Compromise.

On a recent trip to China, President Barack Obama had the opportunity to pressure the country's officials to end their support for totalitarian regimes, as he promised he would on the campaign trail.
 
Obama started the process, but hasn't accomplished his goals yet.
 
He and Chinese President Hu Jintao discussed Iran's nuclear proliferation efforts.
 
"We both stressed that to uphold the international nuclear nonproliferation regime and to appropriately resolve the Iranian nuclear issue through dialogue and negotiations is very important to stability in the Middle East and in the gulf region," Hu said. 
 
But Hu gave no signals that he would support sanctions to pressure Iran to curtail its nuclear ambitions. Iran is China's third largest foreign supplier of oil, and China has recently invested in natural gas projects there.
 
The economic ties between Iran and China have made the Chinese "less enthusiastic, historically, about sanctions," said Jeff Bader, senior director for the National Security Council for Asian Affairs. "The Chinese clearly are hoping that there will be some sort of a resolution on this Tehran research reactor that will not require going to the U.N. Security Council. But the president did talk to President Hu about the possibility ... that we will not reach resolution of this issue and we may have to go to track two and greater pressure. I would not say that we got an answer today from the Chinese, nor did we expect one on the subject."
 
Beyond that, the duo spoke obliquely about human rights, touching on China's relationship with Tibet. There's no indication from press briefings or statements from the trip that Obama and Hu broached the subjects of Sudan, Zimbabwe or Burma (also called Myanmar) where China also has significant economic interests.
 
So, Obama used his trip to China to open discussions about human rights and specifically about China's relationship with Iran. But he got no commitments from officials there, so for now, we're just moving this one to In the Works.