Radishes are crisp root vegetables with a pungent, peppery hotness that varies from mild to assertive depending upon the variety. They are usually eaten raw on their own or in salads. The large Asian daikon is pickled and mixed into relishes and stir-fries. Select firm, crisp radishes. Refrigerate without their leafy tops. Small radishes keep for up to 4 days, larger ones for up to 1 week.