Back-breeding is scientifically very controversial because extinct species or breeds cannot be truly "re-created". But the matter is so fascinating that often the recreation of extinct breeds is attempted. Perhaps most famously are the Heck cattle, the result of the attempt to back-breed the aurochs.
A few dedicated breeders in Switzerland and South Tyrol are back-breeding the Tyrolean chicken, which went extinct about 110 years ago. Those who want to participate in the project are welcome.