“Notice and takedown” refers to the particular sort of cease and desist letter associated with the U.S. Digital Millennium Copyright Act.
An Internet entity ( such as YouTube), upon receiving notice that it is hosting or otherwise making available a copyrighted work, can avoid liability for infringement by immediately taking down the copy of the work in question.
These notices are often criticized because their process strongly preferences rightsholders, who can effectively shut down any and all uses of their work, whether fair, permissible or not, since most posters will not bother to challenge a takedown notice with a counternotice.
Counternotice
The response to a DMCA takedown notice.
A counternotice is the action taken by the person who originally posted the work that was taken down under a DMCA Section 512 “notice and takedown”. If the poster believes that the work was used legitimately, they can inform the host, who then are required to put it back up, and notify the alleged rightsholder that the copyright has been challenged.
The process for challenging takedowns with a counterntice is much more time-consuming and lengthy than that for a takedown itself, leading some to criticize the system as unfairly favoring alleged rights-holders, creating a legal avenue for private censorship of speech, and confronting Internet hosting sites with skewed incentives.
“Putback”
When a website that took content down in response to a DMCA takedown notice puts it back up after receiving a counternotice.
“Putback” refers to when an Internet content host, such as YouTube, having received a “notice and takedown” and then a “counternotice”, puts the possibly infringing content back online, pending a review of its copyright status.