The first is In Our Time, which has started a five part series about the human invention of writing and how writing and its innovations have had a fundamental impact on human history. Subscribe to In Our Time's feed and look for the episodes about The Written World.
The second is a sub-series in the China History Podcast which has been going on for 7 episodes already and is still running. Laszlo Montgomery is telling us the biography of Deng Xiaoping and this is the best introduction to recent Chinese history I have had in a long time. (feed)