Pokemon Go looks to be introducing the legendary Mew through a new quest system coming "later this week".
As detailed on the Pokemon Go blog, Field Research and Special Research are two new types of quest, which offer rewards for completing given objectives.
Field Research quests are earned by interacting with PokéStops, which will now grant you small tasks like capturing or battling specific Pokemon. Special Research "may be requested by Professor Willow himself" - while we don't have full details, that's presumably objectives given to all players simultaneously.
Both Research types grant rewards upon completion, "including a variety of useful items and even encounters with certain Pokémon", with rewards increasing depending on how difficult the task was.
Source : IGN.com