China

China was the main enemy of the United States during the Great War.

The president of China in 2073, and probably until 2077 was called Xin.

It seems that in the 21st century, the Soviet Union lost its position of the dominant communist country to China. Curiously, the only mention of China being communist in any of the Fallout games is in the dialogue with Enclave President Dick Richardson, who calls the Chinese "damn Reds". It also mentioned as such in MCA's Fallout Bible Timeline. It is unknown exactly what kind of political structure the Chinese adhered to. It can be assumed that China as some kind of communist country suits the Fallout setting best, however.

Talking about China political system it could be so called communism or market communism like nowadays (2007 year). Keeping it short it means:
 * communist party dictatorship (about 50-60 milion members - c.a. 5% of population),
 * limited free market economy, benefiting mostly for communist party members and their affiliates,
 * most part of population socialy excluded (particulary peasants on a province).

China shows up in Fallout's history notes as the biggest competitor of the United States, not just in military, but likely also economically and scientifically as they attempted to be the first to drill the last oil resource in the world. It is implied that Americans sabotages this attempt and that without such sabotage the Chinese would've been first. The Chinese also try to keep pace on power armor developments, though how much they managed this is unknown.

It is a known fact that China invaded Alaska, though it is disputed in which year (Fallout Bible: 2059 or 2066, Sierra Depot: 2077), but the exact details on China as a nuclear power are sketchy at best. It is not actually known how much nuclear power China brought to the final blasts of the Great War or even if it was the only country (or even one of the countries?) throwing bombs at the United States, who was at that time in dispute with many countries

Incursion to Hoover Dam
The Chinese solution to invasion by U.S. forces in power armor was its Hei Gui stealth armor, worn by elite Chinese "Black Ghost" counterinsurgency/terror units.

Shortly before the big war started, a Chinese infiltration and sabotage team discovered the Hoover Dam secret geneticslaboratory (Classified Sub-Level 1C) and tried to destroy Hoover Dam, so the genetic work could never be used against them. Some of the Chinese stealth soldiers made it into Sub-level 1C, while others were planting bombs in the main generator rooms (Scum Pits). One of the bombs went off prematurely and alerted all of Hoover Dam, including the guards in S1C. Things become cloudy in the reports due to the chaos that ensued, but suffice it to say that the Chinese were defeated, the generators were heavily damaged, and S1C was compromised. A couple of Chinese stealth solders and four scientists were trapped in S1C after the hatch was sealed. The Prisoner can find this soldiers there and use the materials from their stealth armor to make own armor (Hei Gui armor as possible part of equipment is confirmed by one if van Buren screenshots also).

Shi
Xian, one of Boulder scientists, grew up in San francisco among the Shi.

The Shi inhabitants of San Francisco (or more specifically, Dr. Fung) claim to be descendants of a crashed Chinese Navy submarine Shi-huang-ti. The submarine was intended to be armed with conventional missiles (it was supposed to play a larger role). The remains of this vessel were used to help build the Palace and ship AI was established as the Emperor for the Shi.

The Shi perform dangerous science experiments and have access to destructive and advanced weaponry and manufacturing facilities.