A pair of advocates—they do legitimate research too, but their ardor is so intense, it’s hard to call them scientists—believe that they will, within their lifetimes, make ours the first generation of humans to live forever.

Their quest is elegantly laid out in The Immortalists, a new documentary making its way around the film festival circuit. The Immortalists follows the triumphs and tragedies of three years in the lives of William H. Andrews and Aubrey de Grey, two men who prove just as interesting as the work they’re doing. The Immortalists is really a film about death, not life, which is what makes it so fascinating.

Here’s the trailer:

The goal of Andrews and de Grey is not merely to extend life, but to actually reverse the aging process. “Once we are really truly repairing things as fast as they go wrong, game over,” de Grey says in the film. “We will have the ability to live indefinitely.”

The mechanisms by which each man proposes to end death are radically different. Andrews suggests that in order to lengthen our lives, we may have only to extend the length of our telomeres, which are caps on the end of our DNA that shorten as we age, leading to the breakdown and demise of cells. This mechanism for extending life has the advantage of a potentially straightforward solution: If we can find a pill that lengthens telomeres, we’ve won. Andrews spends the duration of the film searching for one.

De Grey, a theorist who comes across as the better scientist despite his lack of experience “at the bench”—scientist parlance for doing research in a lab—disagrees with Andrews. While his solution to mortality isn’t as clearly articulated in the film, it seems to line up with the strategy articulated by the dean of transhumanism (a movement that aims to remove the limitations on human existence), Ray Kurzweil: Stay alive until microscopic robots that swim through our bloodstream and physically repair our cells are invented, in 20 or so years.

All this may sound crazy, but de Grey has convinced Silicon Valley luminaries such as PayPal co-founder Peter Thiel to give him millions of dollars to fund a full-fledged research foundation devoted to testing his ideas.

What will we do when some portion of humanity refuses to die?

The science behind this sort of thing is extremely controversial—and so are its philosophical implications. It might seem premature to start talking about what we’ll do when the day of the undead finally arrives, but after spending two hours with Andrews and de Gray, I came out convinced that this is a conversation at least worth starting.

David Alvarado, who made The Immortalists with Jason Sussberg, described a similar pivot to me after the film’s premier at South by Southwest. He said he went into this project feeling skeptical of the science behind life extension. Three years and countless hours of filming later, however, it struck him that, eventually, we will radically extend human lifespans—it’s just a question of when.

If humans could live forever, it would transform our civilization in ways more profound than just about any other technological breakthrough. Lifelong marriage—already on the ropes in the age of ever-lengthening lifespans—would cease to make sense. Overpopulation could become an even more significant issue than it is now. The cost of war might have to be re-evaluated. We could live long enough for humans to reach other stars. Young people might find themselves unable to compete in an ossified job market, full of people with centuries of experience.

The Immortalists poses a straightforward question: Why shouldn’t we cure death? But the answer to that question depends on who is asking it—any individual one of us, or all of us.