At any given time a whole bunch of cells in your body need to be destroyed before they cause harm - cells that are past the productive stage of their life cycle and have become senescent, cells that are damaged and malfunctioning, and so forth. The majority of these cells are indeed destroyed, either by the immune system or through self-destruction mechanisms that evolved to trigger when vital cellular processes begin to run ragged. But this protective culling fails with age, and the accumulation of cells that should have been destroyed but were not is one of the driving forces of degenerative aging.
This fact is reflected in the proposed apoptoSENS research program, one of the seven branches of the Strategies for Engineered Negligible Senescence. Where the body isn't keeping up with cells that should be destroyed, appropriate forms of biotechnology can could be developed to perform this necessary work - and thereby remove and reverse this contribution to aging. The first array of therapies will probably look much like the targeted cell killing strategies under development in the cancer research community: using bacteria, viruses, nanoparticles, or the patient's own immune system to selectively seek out and destroy cells based on their surface markers.
I see that recent research adds weight to proposals for therapies that will eliminate senescent cells:
Scientists at the Mayo Clinic, in the US, devised a way to kill all senescent cells in [mice genetically engineered to age more rapidly than normal, and therefore accumulate senescent cells more rapidly than normal]. ... when they were given a drug, the senescent cells would die. The researchers looked at three symptoms of old age: formation of cataracts in the eye; the wasting away of muscle tissue; and the loss of fat deposits under the skin, which keep it smooth. Researchers said the onset of these symptoms was "dramatically delayed" when the animals were treated with the drug. When it was given after the mice had been allowed to age, there was an improvement in muscle function.
[The study] suggests if you get rid of senescent cells you can improve [physical traits] associated with ageing and improve quality of life in aged humans.
The caveat here is that these are not normal mice. Animals that suffer accelerated aging are used for the standard cost effectiveness reasons: the researchers were already working with the breed, effects will be easier to find, and can be found in a shorter period of time. Now that the researchers have an effect and a mechanism by which they can reliably destroy senescent cells, the next step is to repeat the study in ordinary mice and see what happens - which will of course take a few years if they want to evaluate the effects on life span as well as health, risk of age-related disease, and so forth.
Here's a link to the research paper and a little detail on how the authors are clearing out senescent cells:
Senescent cells accumulate in various tissues and organs with ageing and have been hypothesized to disrupt tissue structure and function because of the components they secrete. However, whether senescent cells are causally implicated in age-related dysfunction and whether their removal is beneficial has remained unknown. To address these fundamental questions, we made use of a biomarker for senescence, p16Ink4a, to design a novel transgene, INK-ATTAC, for inducible elimination of p16Ink4a-positive senescent cells upon administration of a drug.
The mice used were BubR1 mutants, and you can find an interesting article on that topic at the laboratory website.