TechCrunch writes:

When trolls barge into people’s notifications with offensive replies or user names, those legitimate users might not keep coming back to Twitter. So today the company rolled out new tools to help you silence the riff-raff. There are now options to mute notifications from newly registered accounts, people you don’t follow and people who don’t follow you. These can be configured in the Notifications -> Settings -> Advanced Filters section of Twitter.

You can read more here.