Wow, my aim was really to be strict about the terminology and always talk about Beijing/PRC or Taipei/ROC, but I noticed that I was saying "China" and "Taiwan" a lot of the time. Lucky I'm not trying to be the President, eh?
I'm sorry it's so long, but on the other hand I think I speak pretty slow, so it's probably pretty amenable to sped-up listening. :-)
Or, you can skip ~27 minutes in to go straight to my overview of the current situation, without the "short" background.
Also, pardon my pronunciation of Chinese names, which is an unpredictable mix of Cantonese, Cantonese-accented Mandarin, Mandarin and English.
Background:
(Image license: public domain)
1644 Qing dynasty
1868 Meiji Restoration
1871 Imperial Japanese Army
1895 End of First Sino-Japanese War
Treaty of Shimonoseki, annexation of Formosa/Taiwan
1905
End of Russo-Japanese war, birth of Kwantung Army
Don't mix up Kwantung/Guandung and Guangdong! One is in Manchuria in the north-east, one is near Hong Kong in the south ...
Korea a Japanese protectorate
1910 Japan annexes Korea
1911 Xinhai Revolution
1919
End of World War I
Japan receives Germany's Chinese concessions
Kuomintang founded
1921 Communist Party of China
1924 Mongolian People's Republic
1925 Death of Sun Yat-sen
1928 Northern Expedition
1932
Mukden Incident
Manchukuo
1936 Xi'an incident (don't mix up general Chiang and general Zhang!)
1937 Japanese invasion, fall of Nanking
(Image license: CC-by-SA, Wikipedia users Rowanwindwhistler and W.wolny, based on public domain work created by the US federal government)
1945