In an effort to be more transparent with its massive user base, Twitter will no longer delete tweets that have received copyright violation claims. Instead the company will take a less drastic approach, replacing the content in question with a message explaining that it's being withheld due to a complaint. Both text and images can be blocked through the new technique but details surrounding the offending tweet will remain preserved and publicly visible. Any retweets of the original post will also reflect the withheld status.
Further, Twitter says it will continue providing Chilling Effects with a copy of every DMCA takedown request, regardless of whether they come from a huge corporation (i.e. Activision combatting pirated copies of Call of Duty: Black Ops II) or individual users — like this recent complaint of a reposted personal photo. If you've been falsely hit with a copyright notice, your avenues for appeal remain the same: file a counter-notice with Twitter, which can lead to the tweet's restoration after 10 days if the rights holder decides against pursuing things further.