The jellyfish Turritopsis nutricula is biologically immortal and could, under ideal conditions, live for 1000s of years. After sexually reproducing, this jellyfish can revert back to the immature polyp stage (back into a “child”). The jellyfish can still die due to predation, but aging is not a problem for it. The exact mechanism for this is not yet well understood. Article on aging and the immortal jellyfish
EDIT: More credible sources, as the first one I posted is a bit sketchy, as pointed out by /u/SirT6 below.
Note: The last article uses Turritopsis nutricula instead of Turritopsis dohrnii but it’s now thought that the two species names may refer to a single species.
This species of jellyfish is the only animal known to be able to revert to an immature state after reaching sexual maturity. To begin we’ll need a quick understanding of the jellyfish lifecycle. They start as a free-swimming larva and then develop into a sessile polyp (similar to a sea anemone). Polyps are colonial and can asexually produce medusa (asexual reproduction results in a clone). Most medusa (the stage that looks like the jellyfish you picture in your head) die after releasing sperm/egg, but Turritopsis nutricula can return to the polyp state after producing sperm/egg through a process called transdifferentiation. Transdifferentiation is a change of well-differentiated cells (cells with specific jobs) to other cell types (different jobs) by returning to a state of undifferentiation (cells with no job). Stem cells are a kind of undifferentiated cells, but it is unclear if they are involved in the transdifferentiation of Turritopsis nutricula. Transdifferentiation is usually only seen in regeneration, but this jellyfish has managed to use it to revert to an earlier form of life. (source 1)(source 2)
While Turritopsis nutricula is the only known animal to revert to an immature state, there are other examples of biological immortality. To be clear biological immortality means that likelihood of death does not increase with age. Wiki page on biological immortality