Aubrey de Grey and Ray Kurzweil suppose that if things go really well we will be able to use biomedical technology and nanotechnology, repsectively to reverse and/or eliminate biological aging in humans and other animals. This is different than immortality.
Aubrey de Grey’s reasoning is that diseases are bad because they kill humans, so we try to cure disease. Therefore, since aging kills humans, aging is bad, and we should try to eliminate and/or reverse the aging process.
Some estimates are, that if things go really really well, then we could perhaps have this accomplished in about 22 years from 2010.