It depends on whether they’re ripe. Unripe peaches, which don’t feel soft when you gently press with a finger, should be left on the counter to continue ripening. Once they’re ripe, you need to eat them, use them in a peach recipe like this one, or put them in the fridge to slow their ripening. They’ll only last in the fridge for a few more days at most, so only plan on buying or picking the number of peaches you need. (Of course, if you have a peach tree just busily cranking them out in your backyard, you’re going to need some friends…or to host a peach desserts party at your house.)