Last month I pointed out an interesting article on regeneration in the zebrafish brain. Zebrafish, like a number of lower animals, have far greater regenerative abilities than we mammals. They can regrow fins and even large portions of some of their major organs. As is the case for salamanders, there is a research community working on understanding the mechanisms of this regeneration, with an eye to seeing whether it can be brought to humans anytime soon. One school of thought suggests that we and other mammals still possess the necessary biological machinery for regeneration of limbs and organs, but it is buried and inactive - after all, just like the fish, we grow from embryos. So there is at least one program for growing limbs and organs hidden in there somewhere.
Nonetheless, it remains to be seen whether it is in fact the case that a mammal can be made to regrow major body structures by following this path of salamanders and fish: there are reasonable arguments to be made for both yes and no, and it's still too early to say which it will turn out to be. There is no necessary reason for limb regeneration in one species to be in any way present but dormant in another, and there is no necessary reason for limb regeneration to be some form of re-running of the initial program of embryonic growth. These could all be different, distinct processes - and for that matter, there could be distinct, different processes of regrowth in different species with these strong regenerative abilities. Biology is always more complex than you'd like it to be.
Putting all this to one side, there is another interesting reason to study regeneration in zebrafish - their ability to regrow tissue and heal wounds doesn't decline all that much with age. See this open access paper, for example:
The zebrafish is a widely used model animal to study the regeneration of organs, such as the fin and heart. Their average lifetime is about 3 years, and recent studies have shown that zebrafish exhibit aging-related degeneration, suggesting the possibility that aging might affect regenerative potential. In order to investigate this possibility, we compared regeneration of the fin and heart after experimental amputation in young (6-12 month old) and old (26-36 month old) fish.
Comparison of recovery rate of the caudal fin, measured every two or three days from one day post amputation until 13 days post amputation, show that fins in young and old fish regenerate at a similar rate. In the heart, myocardium regeneration and cardiomyocyte proliferation occurred similarly in the two groups.
Moreover, neo-vascularization, as well as activation of fibroblast growth factor signaling, which is required for neo-vascularization, occurred similarly. The epicardial tissue is a thin layer tissue that covers the heart, and starts to express several genes immediately in response to injury. The expression of epicardial genes [in] response to heart injury was comparable in two groups. Our results demonstrate that zebrafish preserve a life-long regenerative ability of the caudal fin and heart.
More or less everything I said above about limb regrowth applies to the preservation of regenerative capacity with aging. Perhaps there is something here that can be brought to humans in the next few decades, or perhaps not and these are such different biological systems that there is little to be done with the knowledge that will be gained - it is too early to say which way that will go.