There are some animals that don't "age" like we do. These animals can live indefinitely, until they are eaten or die in some accidental way.
Aging is a set of complex bio-physical-chemical processes. We have actually made a lot of progress in recent decades understanding how this happens. There is no fundamental reason we won't be able to better understand these processes and then mitigate them heavily, if not entirely.
Aubrey de Grey is one of the scientists leading these efforts and his work, along with others, is very interesting. It seems to me there is real potential here. There are many difficult hurdles, but I find it plausible we might overcome them to an extent where it is possible to significantly extend the human lifespan.
If course, if this actually happens, there will be massive social, political, and economic consequences. I'm not exactly sure how that would play out. I'm a bit of an optimist, so I imagine there would be some sort of new non-dystopic paradigm that arises.