Around that time, the United States also announced its plans to withdraw all its military personnel from Taiwan. However, the Taiwan Relations Act passed shortly thereafter continued to ensure American aid in the defense of Taiwan.

In late 1978, China's new leader Deng Xiaoping decided to open the country up and advance reforms. The following year, Deng made a trip to the United States, becoming the first Chinese top leader to visit the U.S. since the founding of the People' s Republic.

"I think it really made an impression when Deng Xiaoping came to the United States. A picture I remember is Deng Xiaoping with a cowboy hat. Maybe because in that sense he was kind of colorful," Robert Tansey recalled.

The story that followed is the leapfrog growth of China's economy for three consecutive decades, in which the United States played a major role, both as a key trading partner and investor.

The last 30 years also saw an explosion of cultural and educational exchange. Many people from the United States have come to China to study and work, but even more Chinese have gone to the United States for those same reasons.

According to a report published by the Institute of International Education, in partnership with the U.S. Department of State's Bureau of Educational and Cultural Affairs, the number of Chinese students studying in U.S. universities was almost 158,000 in the previous academic year.

In 1993, the Tanseys were able to satisfy their long-brewing interest in China when Robert Tansey was posted to the U.S. Embassy in Beijing.

In 1999, Robert Tansey completed his diplomatic service in China. However, after retiring from the United States Foreign Service, he and his wife came back to Beijing in 2010.

"I had kind of a dream, or an idea, that I would come back to do something meaningful. So I started looking for that," he said.

Tansey is now working with the Nature Conservancy, an American environmental body that began operating in China in 1998. His wife Stephanie established a primary and secondary school in Beijing in the

1990s that emphasized cross-cultural communication and collaboration and she has been active in the field ever since.

"We had team teachers, one American and one Chinese in each classroom. We also did things with other Chinese schools. These things led to my better understanding about how to collaborate and how to work better together," Stephanie said.

The Tanseys are just two of the millions of Americans and Chinese who have helped build a strong, practical link between China and the U.S.

Over the years, they have also noticed how Americans' perceptions of China have changed dramatically as China's economy has grown and more information about China has become available.

"People were getting the idea that China was really growing, that China was going to be a major economic power," Robert said. "There was a lot of appreciation of China's rising economic role and the opportunities that presented."

Stephanie believes Americans really respect China more and the Chinese people more.

Last week, Chinese Vice President Xi Jinping paid an official visit to the United States. Xi's visit attracted a lot of attention from U.S. media, who portrayed it as setting the tone for bilateral relations over the next decade.

Mike Chinoy, professor of media at the University of Southern California, said the tone of American media on Xi's visit is positive.

Chinoy believes the media will play a vital role in future relations between China and the U.S. and that the changing media landscape also means there are many more information outlets now such as Internet, blogs and microblogs.

Much as Chinese and Americans learn more about each other through the media, more and more of them are learning about the other country firsthand.

According to the China National Tourism Administration, in 2011, more than two million Americans traveled to China. At the same time, the U.S. was a major destination for Chinese tourists.

"China has a little over 30 provincial-level jurisdictions. I've been able to visit 26," said Robert Tansey. "When I look at the map of China now, I think, 'oh, there are still five or six provinces I haven't been to. And I want to get there.'"