Describe how China and Japan dealt with the arrival and continued presence of foreigners in their lands from the 1500s through the 1900s.

When Europeans began arriving in East Asia in the sixteenth century, China and Japan at first dealt with the situation in similar ways. There was much confusion and resentment over European practices. Christian missionaries flooded into both countries, but in the early seventeenth century, Japan began a massive effort to repel Christianity and European influence, effectively isolating itself from Europe for the next 200 years.
Meanwhile in China, European missionaries were welcomed in the Chinese imperial court in 1601 and acted as advisers there for the next 150 years. Trade relations between Europe and China were good until China tried to ban the sale of opium. That led to the Opium War of 1839, in which China was easily defeated by superior European military capabilities and forced to sign favorable trade deals and allow the Europeans access to ports.
Soon Japan's period of peace and isolation came to close, as it opened its ports to the Europeans and Americans. At this time Japan began a decades-long effort to industrialize its economy, educate its population, and strengthen its military so that it could compete with Western nations. In the late nineteenth century it revised its trade treaties with Western nations, effectively putting itself on equal ground with them. It then defeated Russia in a 1904 war, establishing itself as a world power.
China was not as successful as Japan at resisting. Indeed, Japan even joined Western nations in carving up China into "spheres of influence" in the late nineteenth century. The Qing Dynasty fell in 1911, and China entered a period of prolonged turmoil and civil war that would not be settled until the Chinese Communist Party established the People's Republic of China in 1949.
http://afe.easia.columbia.edu/timelines/japan_modern_timeline.htm

http://blogs.bu.edu/guidedhistory/moderneurope/tao-he/