A living Pokédex is a game which not only has a complete Pokédex, but has one of every 493 species of Pokémon stored in its PC boxes as well. It is considered a holy grail among some collectors. Among others, it is considered a waste of time and box space.
Perhaps one of the most challenging questions is not how to obtain a living Pokédex, since that is mostly a matter of patience and access to multiple games, but rather what to do with the living Pokédex once it is complete. In particular, in this instance, or with any large Pokémon collection in general, the question of storage arises.
In Generation III, Pokémon Box was introduced, which allowed players to store their large collections without worrying about taking up PC space; in fact, players were rewarded for transferring more Pokémon into Pokémon Box, making the living Pokédex goal more appealling.
However, since the onset of Generation IV, no new edition of Pokémon Box has been released, stunting the collection size of many collectors. Those who aim to complete a living Pokédex, particularly one with form differences, must do so while sacrificing most of their box space which could be used for multiple rare and valuable Pokémon, shiny Pokémon, and trained Pokémon. Of course, these other Pokémon could be traded to another game, which players who aspire to obtain a living Pokédex probably already have in order to obtain version-exclusive Pokémon.