We know these things about Twitter relating to censorship:
They have shut down Twitter accounts for abusing the TOS, and this process is on a case-by-case basis, and can affect well-known users such as Milo Yiannopoullous and Martin Shkreli:
http://www.breitbart.com/milo/2016/07/19/breaking-milo-suspe...
http://www.breitbart.com/tech/2017/01/08/pharma-legend-marti...
Twitter also deletes content in response to valid legal requests and copyright claims, according to their own transparency report:
https://transparency.twitter.com/en.html
We also know that Twitter has applied crowdsourcing/human editing to search query analysis:
http://blog.echen.me/2013/01/08/improving-twitter-search-wit...
I suspect that Trending Topics also has some curation, or at least a manual blacklist, but couldn't find official mention of that.
We also know that Twitter has been sensitive to the tension between being an unfiltered source of information and a platform that amplifies abuse. In January, the company admitted that it "didn't move fast enough" in dealing with abuse complaints:
https://arstechnica.com/information-technology/2017/01/twitt...
In March, they announced new measures for reporting abusive tweets/accounts. Under a heading "Leveraging our technology to reduce abusive content", they describe new ways in which an abusive account can be limited, including suppressing the visibility of tweets: https://blog.twitter.com/2017/our-latest-update-on-safety
So we've seen that Twitter will shut down accounts and tweets based on an interpretation of TOS (i.e. what constitutes "abuse") in ways that not everyone agrees with. At the same time, Twitter knows that its special sauce is unfettered speech, so much so that it was slow to even act on shutting down accounts openly associated with ISIS: https://www.theatlantic.com/international/archive/2016/02/tw...