Storage

In Pokémon Chest you have 50 boxes in the Chest to store Pokémon by default (this can be changed to any amount up to 500) and you can change chests from the Options menu if you need more.

You can store any Pokémon from generation 4 and 5 games in the chest and transfer them back (provided they were in the game you're transferring to).

You can do various things to Pokémon in the boxes including: moving, copying, releasing, dumping, and injecting.

Using Select you can change the cursor mode (explained here)