Your inventory is the place where all items that your character has are stored.
During the battle access to inventory costs 4 Action Points, but can be reduced by perk Quick Pockets. In Fallout Tactics, access to the inventory is free, but various actions in the inventory cost you action points and the vehicles also have inventories.
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Access it by pushing the default button "tab" for PC during the game, B on Xbox 360, and O on PS3. Access to the inventory is free during a fight and freezes the game until you close the inventory. In Fallout 4 the controls on the Xbox One and PS4 are identical to that of each respective console's predecessor.
The items are sorted into weapons, armor, aid, misc., and ammo categories. In Fallout 4, there is also the additional junk category. From the inventory one can change the weapon in hand, the armor they wear, and use food and drugs. In Fallout: New Vegas, one can also put a weapon mod on a weapon and change the ammunition type of the weapon in hand.
Some items also stack on top of each other, giving the appearance that only one item is currently in the inventory. This is the case with binoculars, for example.
Access it by pushing the "select" button for PS2 during the game. Access to the inventory is free during a fight and freeze the game until you close the inventory.
The items are sorted into weapons, armor, items. In the inventory you can change your three active weapons, the armor you wear and use drugs.