Fresh tomatoes should be stored at room temperature until they are fully ripe. Once they are ripe, they can be stored in the refrigerator for up to a week. If you have cut tomatoes, it is best to store them in an airtight container in the refrigerator and consume them within a day or two. To extend their shelf life, you can also freeze tomatoes. To do this, simply blanch them in boiling water for a minute or two, then peel, core, and freeze them whole or chopped.