As you may know, a range of ways to extend life in nematode worms (such as the common laboratory species Caenorhabditis elegans) involve interfering in the operation of mitochondria. This is also true in a range of other lower animals - mitochondrial operation is apparently strongly coupled to the natural range of longevity enjoyed by a given species. But what are mitochondria? They are a roving swarm of tiny power plants, present inside every cell, and inside each mitochondrion there can be found an array of intricate molecular machinery that gives rise to what is called the electron transport chain. This is a critical component in the process of building stores of chemical energy - in the form of ATP - used to power the operation of the cell. It is alterations in the operation of the electron transport chain that can alter longevity for the better in many species.

A recent open access paper digs into other mechanisms that relate to this link between electron transport chain operation and life span, outlining the discovery of a gene that is necessary for that enhanced longevity:

Mitochondria have long been associated with aging and age-related diseases. Recent research has shown that a slight dampening of mitochondrial function can dramatically increase the lifespan of a wide range of organisms, suggesting that a similar mechanism likely operates in humans. The molecular basis of this observation is largely unknown, however. Uncovering the genes that allow altered mitochondrial function to impact longevity will give us important new insights into how mitochondria affect the aging process and will pave the way for future therapeutic developments aiming to improve healthy aging and to treat age-related diseases.

Here, we used an RNAi screen in the genetic model organism C. elegans, a nematode worm, to uncover how altered mitochondrial function can modulate longevity. We found that in order for mitochondria to affect lifespan, they must communicate with several unique transcription factors in the nucleus. Notably, we discovered that the putative homeobox transcription factor CEH-23, which has not previously been implicated in longevity determination, is able to respond to changes in mitochondrial function and in turn causes an extension in lifespan. ... ceh-23 expression levels are responsive to altered METC, and enforced overexpression of ceh-23 is sufficient to extend lifespan in wild-type background.

So it looks like some form of programmed response causes the life extension in these methods, and manipulations of the electron transport chain only trigger that response - which is interesting. Not what you might expect, given all the other ways in which mitochondria touch on aging, such as through accumulated damage to their DNA.