Asia

Asia was a continent of the planet Earth. (TV: The Dalek Invasion of Earth)

Early history
According to Barbara Wright, the Mongols conquered all of Asia under the rule of Kublai Khan. Indeed, in 1289, a vizier introduced the Khan as the "ruler of Asia, India, Cathay and other territories." While playing backgammon with the First Doctor, the Khan found himself owing half of Asia to him. (TV: Marco Polo)

20th century
During World War II in Asia, better known as the Pacific War, (COMIC: 4-Dimentional Vistas) Japan's war aim was to unite the continent under the Asian Co-Prosperity Sphere. (PROSE: The Face of the Enemy) Their ambitions ultimately spread war throughout the continent, with attacks in China, Manchuria, (PROSE: The Shadow of Weng-Chiang, Log 384) the Philippines, (PROSE: Happily Ever After Is a High-Risk Strategy) Singapore, (AUDIO: The Forsaken, The Girl Who Never Was) Burma (PROSE: Just War, The Scales of Injustice) and other Pacific Islands before Japan surrendered in 1945. (PROSE: Endgame)

During the Korean War, Red Chinese soldiers entered Korea from Manchuria to fight the American forces in 1950. (COMIC: The Good Soldier)

Later, during the 1960s, America was involved in a conflict in Vietnam. (AUDIO: Renaissance of the Daleks, TV: The Impossible Astronaut) The war ended on 23 February 1973, with no clear victor. (PROSE: Nuclear Time)

In the late 20th century, amidst growing tensions between Russia and China, fighting broke out in southern Asia and South America before Sir Reginald Styles was able to negotiate peace, cooling the crisis and preventing World War III, with the Third Doctor preventing an alternate timeline where Styles was assassinated and war did indeed come to pass. (TV: Day of the Daleks)

In 1979, China invaded Vietnam. (TV: Tooth and Claw)

21st century
In the early 21st century, a Skullion ship crashed in central Asia on Earth and its crew were sold into slavery. (TV: The Man Who Never Was)

In light of Miracle Day in March 2011, Asia reported no deaths along with the rest of the world. (TV: The New World)

In 2015, North Asia was among the places where newly-hatched Zygons were settled across the world as part of Operation Double. (TV: The Zygon Invasion)

Later history
Following the plague sent by the Daleks during their 22nd century invasion of Earth, a majority of the population of Asia died before a cure was found. (TV: The Dalek Invasion of Earth) A human resistance movement was later formed in China against the occupation, but was crushed by the Daleks within days. (AUDIO: Masters of Earth)

At one point, Asia was home to one of the five ioniser bases keeping back the glaciers of the second Ice Age. (TV: The Ice Warriors)

Alternate timeline
The First Doctor warned Steven Taylor that even saving the life of a child in the 1240 siege of Kiev could change history into a future where an atomic war consumed most of Asia. (PROSE: Bunker Soldiers)

Asia appeared on General Logan's map of the eastern hemisphere in an alternate 1855. (TV: War of the Sontarans)

Behind the scenes
According to the "Earth-Skaro Timescale" of Terry Nation's Dalek Annual 1976, Asia was struck by drought, floods and famine in the Earth year 1974. Meanwhile, in Skaro-year 10,959, the Daleks had stationed a weather control satellite in Earth's orbit.