This is an entire category unto itself with no particular end in sight.
Directors are the best way to start:
China
~ Feng Xioagang
~ Zhang Yimou
~ Wong Kar Wai
~ Jia Zhangke
~ Ang Lee
~ John Woo
Korea
~ Park Chan Wook (brilliant, mad, poetic genius)
~ Kim Ki-duk
~ Lee Chang dong
~ Kim Jee-woon
Japan
~ Yasujirô Ozu
~ Hayao Miyazaki
~ Masaki Kobayashi
~ Akira Kurosawa (FILM 101!!!)
In particular, the Korean Film industry is going through a creative boom. A country of only 40 million people is creating films all demanded at Venice, Berlin and Cannes. Figures such as Jeon Do-Yeon, Son Ye-Jin and Byung-Hun Lee are credible, talented actors of the highest order.
Check out 'The Wailing' (Ridley Scott wants to do an English Language remake). 'Burning' (presently playing at TIFF) and 'The Villianess' (hold on to something).