This is a very nice summary of the evolution of aging which describes mutation accumulation, which is an extension of Medawar’s declining power of selection hypothesis. The link above does a nice job of explaining the concepts.
Antagonistic pleiotropy is the concept that a gene for survival or a gene that promotes
reproduction early can be selected for even if it kills you at a later
age. So selection favors juvenile survival at the expense of old age survival. This hypothesis recognizes that most traits have both costs and benefits, and are tradeoffs. The tradeoff in antagonistic pleiotropy is improved health in youth, but disease in old age.
Haldane and Medawar proposed the declining power of selection hypothesis of aging. This proposes that genes for maintenance and repair of the body are selected for more strongly at early ages (pre-reproduction) than after reproductive age. For this: imagine a hypothetical gene that prevents cancer at age 10 and another gene that prevents cancer at age 100. The gene that prevents cancer at age 100 will not have any effect most of the time because most people are dead by age 100 (this remains true even if you take senescence out of the equation – random accidents will claim many lives). The gene that affects 10 year olds is more likely to be expressed and have a benefit simply because most people are alive at age 10. Therefore the old-age gene will be invisible to natural selection, the gene that affects 10 year old will be subject to positive selection.
Medawar extended his idea to include mutation accumulation. This idea posits that the body accumulates deleterious mutations at late ages that, because of the declining power of selection, are not selected against, and thus accumulate. In wild populations, not enough organisms reach advanced age, so these mutations are invisible. If allowed to achieve advanced chronological age, these mutations exert damaging effects, reducing fitness and contributing to senescence.
The disposable soma hypothesis is another idea to explain aging. This hypothesis recognizes that the nonreproductive part of the body (the soma) exists only to support the reproductive part of the body. At any moment in time an adult can devote energy to the maintenance of the body or to reproduction. Put simply, after successful reproduction, the soma is “disposable”, and genes are passed on. This tradeoff is vividly illustrated in adult salmon, which appear to do all their aging at once, immediately after a single reproductive effort. In many animals, bearing offspring shortens lifespan. There is some evidence of this in humans too.