While most people believe the best possible life they could lead would be an immortal one, so‐called “immortality curmudgeons” disagree. Following Bernard Williams, they argue that, at best, we have no prudential reason to live an immortal life, and at worst, an immortal life would necessarily be bad for creatures like us. In this article, we examine Bernard Williams' seminal argument against the desirability of immortality and the subsequent literature it spawned. We first reconstruct and motivate Williams' somewhat cryptic argument in three parts. After that, we elucidate and motivate the three best (and most influential) counterarguments to Williams' seminal argument. Finally, we review, and critically examine, two further distinct arguments in favor of the anti‐immortality position.