The jellyfish Turritopsis nutricula is one of the few species whose members might be considered immortal, based on what is presently known of its biology. The life course of this jellyfish is very far removed from that of humans; even more so than that of the lobster, another marine species that might be immortal - though there researchers know far too little to make the call one way or another.
Immortality in the sea lasts right up until something larger eats you, of course. The form of agelessness enjoyed by Turritopsis nutricula appears to be an adaptation to periods of starvation: it can retreat to earlier stages of its life cycle, and in the process its cells alter their character in an usual way:
It starts out as a larva that eventually sinks to the bottom of the ocean and attaches to a sturdy substrate and continues development into a polyp that resembles a sea plant. The polyp then matures to become a free-floating medusa, what we commonly recognize as jellyfish resembling an upside down saucer with tentacles. ... However, during times of stress like a shortage of food, Turritopsis responds by beginning to reverse the process before eventually becoming a polyp again. From this point then, it can again develop into a sexually mature medusa when conditions become more favorable. Theoretically, it can repeat this process indefinitely as its cells undergo a process called transdifferentiation, a rare biological process whereby any non-stem cell can become a different cell entirely. It is still unclear whether only specific cells can only become other specific cells or if any cell in Turritopsis has the potential to become any other cell.
Unlike other long-lived or apparently ageless animals, the principle biological process of interest here is transdifferentiation - being able to produce any type of cell from any other type of cell without having to go through intermediary stages such as the generation and differentiation of stem cells. Modern stem cell medicine depends on techniques for controlling and changing the state of cells - to be able to engineer pluripotent cells from ordinary cells, for example, or produce unlimited numbers of a particular type of cell for research, transplantation, and tissue engineering.
When it comes to transdifferentiation, the hope is that we will eventually be able to learn how creatures like Turritopsis skip the stem cell step and go directly from one cell type to another.
Reliable control over that process for human cells would greatly improve the state of the art in the field of regenerative medicine - and in fact research groups in the space are headed in that direction already.