Splatsch: Can someone lighten me a little : I'm not sure to understand perfectly what is this "take down" concept ? Google has to suppress results of researches in his google search ? To ask to sites to stop/suppress the content ? I'm asking because it seems google receive a lot of the complaints. For me take down demand is "suppress the content of this page", but how can be google directly implied ?
The DMCA provides a safe harbor provision for service providers, granting them immunity to liability for copyright infringement that is conducted by others. In the case of your example, this means Google is not liable for search results that contain examples of copyright infringement. However, the safe harbor provisions come with conditions, and one of those conditions is what is known as a takedown notice. Rightsholders can send a complaint to these companies detailing alleged copyright infringement and request the page be removed. Google is not technically
required to comply with these requests, but should it elect not to carry through it would lose the safe harbor provisions and become secondarily liable for the copyright infringement alleged in the takedown notice. Because copyright judgements can be positively massive, denying these takedown requests is actually a huge liability for Google and they only do it in cases where it's very obviously wrong.
As I discussed earlier, there are technically provisions to seek damages from takedown notices made in bad faith, but proving bad faith is so difficult that you will virtually never pull it off. This has created a horrifically lopsided system where rightsholders can send out automated requests with impunity based on nothing but a rough algorithmic match, the service provider faces massive financial risk for backing you up and as such is overwhelmingly likely to block you, and you face an arduous process for reinstatement with a mandatory wait period... and no assurance you won't just receive another takedown again in the future.
It's frankly a ludicrous system that allows powerful corporations to bully individuals and small companies, and provides little to no recourse to those caught as collateral damage.