I know these are two different time periods but I'm curious to both. It seems like Rome ruled the world for a while but I haven't heard anything about other countries during these time periods. I was curious about Asia specifically, and how the cultures might have interacted.
You might be interested in some earlier answers.
On what was happening in China in the time of the Antonines and Severans (by u/Dongzhou3Kingdoms):
On Greco-Roman contact with India and China: