The degree of ripeness of fruit when you buy it determines how long it can be kept. Some fruits ripen relatively slowly after they mature—apples, pears and oranges, for example. Others, such as grapes and berries, are ripe or overripe within a few days of maturity and thus cannot be stored for long.
Fully ripened fruit should be refrigerated immediately, first discarding any overripe or moldy pieces—berries are particularly susceptible to mold. Handle fruit gently, as bruising or crushing encourages rot, and wrap it loosely in a brown paper or plastic bag punctured with holes.