One cause of the physical degeneration associated with aging involves telomeres, which are segments of DNA found at the ends of chromosomes. Every time a cell divides, its telomeres get shorter, and once a cell runs out of telomeres, it can't reproduce anymore and dies. There is an enzyme called telomerase that reverses this process and it is one of the reasons cancer cells live so long.
In November, 2010, researchers at Harvard Medical School announced in Nature that they had administered telomerase to a group of mice suffering from age-related degeneration. The damage went away and the mice didn't just get better; they got younger. Proponents of the Singularity see this as just a natural progression and predict that aging is just another problem that can be overcome, likely in the next twenty to thirty years. I agree.