The Bag is an item introduced in Generation I.
Description[]
The Bag is equipment in every game of the core series. It holds all of the player's items, storing them until the player uses them. When opening the bag, the player can use, arrange, and toss any items except for key items, and register key items for easy access. All the items that the player has on hand will be located in the bag, after Generation II, being placed in the appropriate pocket automatically. Prior to Generation IV, if the Items pocket is full and the player attempts to pick up an item, they cannot store it in their Bag unless they make more space for it, such as by using or discarding items, or putting some of the items into a PC. This was resolved by Generation IV, where the Bag has enough room for every item. The bag menu shows every item, ordered from the first obtained to the most recently obtained.
In Pokémon HeartGold Version and Pokémon SoulSilver Version, items are no longer displayed in a list, but grouped in sections with six items per section. There are additional Poké Balls that can be carried in the bag.
In Pokémon Black Version and Pokémon White Version, items are displayed in a list once again. Items can be reorganized with Select once more, though there is now a button that organizes all items in a section in alphabetical order.