Special Research is a story mode featuring the story of Professor Willow and the task to find rare Mythical Pokémon. This is accessed when Professor Willow has an icon notification at the bottom right of the screen indicating he has a task for you. There are 8 different elements of the story, each with various tasks to complete, all of which getting more difficult with each stage.
Once complete, players then have a chance to get Mythical Pokémon including Mew.
Players can only go through each Special Research story once.