Google has released a new transparency report, which is good. I would rather they put up more of a fight, but there are cases such as court orders which make that problematic.
One interesting part today is the government requests section. You'll see there that the most common type of government request to remove content, by far, is "defamation", which is what despots always say when they censor stuff. What is interesting is if you go down to the United States section, down at the bottom, that Google did, indeed, receive several requests from the U.S. to do this for the same reason, and happily they rejected the requests. But it just goes to show that Americans are not immune to abusing any censorship system that exists.