Mythical Pokémon were originally known in common conversation as "Event Only Pokémon" for a reason. These Pokémon are so rare that they are typically only available through going to an event distribution and either receiving the Pokémon itself, or an item to go get the Pokémon within the wild. Due to the fact that these are typically only from events and have limited distributions, these Pokémon are banned from Battle Tree, Battle Frontier and similar facilities, as well as the Rating Battles in Battle Spot & the Video Game Championships . Several instances of Online Competitions have allowed for the use of these Pokémon. They have typically have base stats that sit around 600, and some even have Form Changes or Mega Evolutions causing stat increases.
The Generation 7 Pokémon games also introduced the first evolving Mythical Pokémon