Aubrey de Grey's proposal for serious anti-aging research, Strategies for Engineered Negligible Senescence (or SENS), is positioned as an engineering project. Aubrey explains why in this manner:
SENS is a detailed plan for curing human aging. SENS is an engineering project, in the same way that medicine is a branch of engineering. The key to SENS is the appreciation that aging is best viewed as a set of progressive changes in body composition at the molecular and cellular level, caused as side-effects of essential metabolic processes. These changes are therefore best thought of as an accumulation of "damage", which becomes pathogenic above a certain threshold of abundance. The traditional gerontological approach to life extension, namely to try to slow down this accumulation of damage, is a misguided strategy, firstly because it requires us to improve biological processes that we do not adequately understand, and secondly because it can even in principle only retard aging rather than reverse it. An even more short-termist alternative is the geriatric approach, namely to try to stave off pathology in the face of accumulating damage; this is a losing battle because the continuing accumulation of damage makes pathology more and more inescapable. Instead, the engineering (SENS) strategy is not to interfere with metabolism per se, but to repair or obviate the accumulating damage and thereby indefinitely postpone the age at which it reaches pathogenic levels.
Human cells are a very complex machine, and thus we as humans are a complex collection of very complex machines. Advances in genetics, bioinformatics, and other fields of modern medicine are beginning to provide the knowledge and tools needed to examine, alter, repair, and extend our cellular machinery.
Consider the thought experiment of a stone age New Guinea tribe given the full output of a modern car factory, but no help from the outside world: no manuals, teachers, explanations, nor understanding. Human nature being what it is, members of the tribe will learn - slowly and through trial and error at first, but increasingly rapidly as time passes - how cars work, how to take best care of a car, and how to repair it, one component at a time. This is exactly the position that the human race as a whole is in with respect to our own bodies. There are more of us, but the task in front of us is vastly harder.
If you're a non-biologist who keeps track of aging research, like myself, you'll probably have a vague idea as to how things fit together inside a cell and in the various theories of aging. You probably also wish that you had paid more attention in class when you were learning about biology. The reality is quite complex; to get an idea as to how complex, you might try the discussions linked below:
Complex or not, finding a cure for aging is "just" an engineering problem, however. It is not mystical, nor is it impossible. It's just difficult. The time taken to produce results depends on our willingness to support and fund research.
Where does cancer fit into all of this? Cancer and aging share aspects of the same cellular mechanisms and biochemistry. Cancer is probably the result of malfunctions in the telomere mechanisms determining cell life spans, and the risk of cancer continually increases with age - perhaps due to the damage already caused by other components of the aging process. This area of biochemistry is under study by a number of groups, and scientists are learning more each year about the mechanisms and biochemistry involved.
Aubrey de Grey's principle objection to an absolute focus on regenerative medicine as the path to longer, healthier lives is that this will do nothing to stop the ever-increasing risk of cancer. Given that cancer is currently the second most common cause of death (and the only reason it isn't the most common is due to society-wide support for resources to be directed towards finding a cure, starting in the early 1970s), any life-extending strategy will fail if we do not develop a cure or preventative therapies for cancer.
This is exactly the same rationale for the fight to cure Alzheimer's - without a cure, this horrible condition will kill us long before we realize the benefits of a healthy life span extended through regenerative medicine.