Onion: Placing your onions inside your refrigerator will eventually end up turning them moldy and soft. According to the National Onion Association in the U.S, unpeeled onions should be kept out of plastic bags and fridge. One of the reasons for this is because unpeeled onions require and need air exposure for maximum life. If you have peeled an onion though, then you should keep it in the fridge, in a covered container.
Garlic: placing garlic in your refrigerator will actually cause it to sprout. The garlic will also get moldy and even rubbery. Moreover, inside your fridge, the look of the garlic will rarely change. This means you won’t be able to tell if it’s any good until you finally slice it open.