Encounters between the United States and China span almost two and a half centuries. Many believe that U.S.-China relations are the most consequential bilateral relationship of our time. My new book, The United States and China: A History from the Eighteenth Century to the Present, explores not only high-level diplomacy but also a range of other human contacts in domestic and global affairs.

As someone who has studied and experienced American-Chinese relations during the last three decades from vantage points in Asia, North America and Europe, I will share here ten observations about the character of those relations.

First, Sino-U.S. relations are a tangle of contradictions. The two countries have been called the "odd couple," by The Economist in late October 2009, and the "power couple" by others more recently.

In 1915, Yuan Shikai, the first president of the Republic of China (1912 - 49), spoke of the dissonance between America's exclusion of Chinese immigrant labor and its Open Door policy in China (see Observation four below): "While America was the only country of the world which denied admittance to our countrymen, it was also the only nation which stood like the Great Wall between China and dismemberment." In contemporary times, the U.S.-China relationship fluctuates between being friends and foes, and strategic partners and rivals, as well as betweem deterrence and engagement, hedging and confrontation, accommodation and friction, and interdependence and independence. Contradictions indeed.

Second, the United States and China are rooted in each other, and not fundamentally worlds apart. Their bilateral relations grew out of private commerce, the Old China Trade, in 1784—which was relatively marginal in politics and the economy at the time-to become the center of their strategic attention. This transformation brought about a web of diplomatic, economic, social, religious, cultural, and military ties that conjoin the two peoples. Today, over three million Chinese immigrants live in the United States. In 2010, China ranked as the fifth-largest destination for American students (over 13,000) studying abroad.

Third, from a long historical perspective, the relationship between the United States and China has passed through three phases, roughly divided in the mid-nineteenth and mid-twentieth centuries. Their relations shifted significantly from interaction between an empire (Qing China, 1644 - 1911) and a young nation-state (United States), to interplay between two nation-states (Qing China/Republic of China 1912 - 49 and the United States of the same period), and then to wide-ranging encounters between a nation-state (People's Republic of China, 1949 - present) and an empire (United States, post-World War II).

The concept of empire in the history of U.S.-China relations has two connotations. When applied to Qing China (1644 - 1911), it refers to the last of China's dynastic empires-one that still evoked the glory of an ancient civilization, but found it hard to understand what nation-states and sovereignty meant until the latter half of the nineteenth century. When used as an epithet for the United States after World War II, empire denotes the proselytizing exercise of national power and influence over other peoples-criticized by some as a deviation from the ideals of America's founding fathers, hailed by others as America's proud mission to make the world a better place for everyone.

Fourth, the two countries are competing for markets, resources, and power on a global scale. Economically, China has been catching up, clashing with America's desire to control change. But, China is not likely to eclipse the United States in the main areas of development any time soon.

America's early experiences in China showed the U.S. conscious pursuit of national greatness as an independent country and its entrepreneurial flexibility and tactical pragmatism. In the latter half of the nineteenth century, rather than following the Europeans and Japanese who scrambled for territories, concessions and spheres of influence in China, the American state championed the Open Door doctrine-free trade and the maintenance of Chinese territorial and administrative integrity. Qing China was forced to submit to the global expansion of capitalism and to manage foreign affairs within an unequal treaty system. A strong central state was considered the key to China's national success, but the pathway to modernization remained elusive, frustrating generations of Qing and Republic of China leaders and elites.

As the Chinese Nationalist government (1928 - 49) set out to modernize the country, its leader, Chiang Kai-shek, looked to the United States to contain Japan's and Russia's imperial ambitions in China. But rival national leaders-in particular, Chiang Kai-shek and Mao Zedong-resisted foreign influence and ultimately upset American and Russian designs for China in post-World War II. In the 1970s, improved U.S.-China relations helped steer China away from the ideology of violent revolution to a belief in prosperity through evolution.

For China and the United States-the world's two largest economic giants-continuous technological innovation holds the key to the future. As China changes from an agrarian, sweat-shop, manufacturing economy to a mature consumer society, its state-sponsored industrialization and overseas investment are widely seen as similar to developmental capitalism in Japan and Europe. Some best-selling authors, such as Michael Lind, advocate this model of growth for the United States, while lamenting America's "lost ten years" in the post-hegemonic twenty-first century.

Fifth, U.S.-China relations involve competing political cultures. America's power in the world derives from the triangular relationship between Providence, wealth, and military force, whereas the ruling party-whether the Nationalist Party (1928 - 49) or the Chinese Communist Party (1949 - present)- together with the Chinese people has been identified as the source of Chinese power. Development and peace are China's theme songs for the twenty-first century; they take their place alongside democracy and freedom, America's most loudly trumpeted values.

Sixth, the United States has been an important model for China. The U.S. role as one of China's models or tutors is perhaps best symbolized by American missionary endeavors in China (1831 - 1951) and the ongoing massive flow of Chinese students to the United States. Beginning in the 1870s, American-and Chinese-sponsored educational efforts cultivated an elite power base in China, along with a belief in American values and influence on China's future, particularly on its intellectual elite.

Seventh, Sino-American contention partly arose from the wide gap between China's and America's concerns expessed in public discourse. Contacts between the two countries over domestic and foreign matters have yielded many images and labels of each other voiced across the Pacific. These perceptions and labels include the China market vs. the U.S. Open Door, red China vs. imperial America, the return of China vs. the allure of America, and the China threat vs. new American imperialism.

I still remember how depressing it was to discover that China was "bad news" on American televisions in 1993 when I arrived in the United States from Beijing to pursue my second Ph.D. It is equally worrisome to me today that America's "pivot," or "rebalancing," to the Asia-Pacific, under President Barack Obama's watch, has been perceived by the Chinese public as an American conspiracy against "peace-loving" China.

Eighth, the United States and China share responsibility for the unsettled post-World War II order in the Asia-Pacific. Long-term stability and peace on the Korean Peninsula, in the South and East China Sea, and over the Taiwan Strait are mutual security interests for both countries in the region.

Ninth, America is the champion at scientific and technological innovation, led both by large corporations and the dirigiste state and protected by a vigorous intellectual property rights regime. For China, science has multiple meanings-from high technology and natural sciences to rationality and fairness of social transformation under Hu Jintao's "scientific view of development" (Kexue fazhan guan). For the founding leaders of the Chinese Communist Party in the first quarter of the twentieth century, Mr. Science was Mr. Democracy's closest companion. The real competition between China and the United States, though, is over how to deal with climate change, ecology, mineral resources, and energy.

Tenth, the "Chinese dream" (Zhongguo meng), put forth by the new leader Xi Jinping, aspires to match the American dream. Before we dismiss it as just another copycat slogan, let us consider that in history, glorifying labels have often switched owners. At least China does not claim to be God's own country. Just yet.