1) In the early 20th century, China was in turmoil following the fall of the last emperor. Sun Yat-sen led the nationalist Kuomintang party and established a government in southern China.
2) In the 1920s-1930s, the Kuomintang and Chinese Communist Party formed an alliance against their common enemies, but later had a falling out and fought in a civil war.
3) By 1949, Mao Zedong had led the Communist Party to victory over the nationalists. Mao established the People's Republic of China, while the nationalists retreated to Taiwan. China was then divided between communist mainland China and nationalist Taiwan.