Dr. Aubrey deGray is a scientist who created the idea of SENS, Strategies for Engineered Negligible Senescence. The main thrust of his idea is that scientists have been focusing on metabolism and pathology, which are extremely complex. What is less complex are the cellular damages that accumulate due to metabolism and lead to pathology. If we focus on these "seven deadly things," we could make drastically more productive use of scientific facilities, research money, and brain capital.
A good page explaining the research behind Dr. Aubrey deGrey's ideas is http://www.sens.org/index.php?pagename=mj_sens_repairing". It explains the seven different types of aging damage that have been discovered so far, and why probably all of the "primary changes in the structure of the body itself" (in aging) have been discovered. Briefly, the seven types of aging damage are:
1) cell loss, tissue atrophy
2) nuclear mutations
3) mutant
mitochondria
4) death-resistant cells
5) tissue stiffening
6) extracellular aggregates
7) intracellular aggregates
I think we could look at the above seven things as the "mechanisms of aging." However, it is true that we do not understand, in detail, the mechanisms of metabolism and pathology. It is probably not a very productive approach to focus on them, either. But that's exactly what most biological scientists and research organizations do, exclusively.
I think it makes more sense to direct research towards work that directly addresses the above seven mechanisms. To do so, young scientists need to work towards that goal. Likewise, the public needs to educate themselves on this issue (SENS or Strategies for Engineered Negligible Senescence), and support research about it.
There are a few organizations actually doing this right now, and the number will surely grow in the future. Currently the ones I know of are:
http://www.methuselahfoundation.org/"
http://imminst.org/"
So, to answer the question of this thread: "In what ways can biology create indefinite lifespans?"
Answer: By developing technologies for repairing, limiting or reversing the seven types of aging damage. That can only really happen if the public becomes aware of this approach.