off most of the dark green top, leaving a leek 6 - 7" long, making it much easier to store. like most vegetables, they don't need to be refrigerated but will keep longer if they are.
another note: if you buy prepared beef or chicken stock and have some leftover that won't be used right away, freeze it, either in small containers, or as cubes using an ice cube tray. when frozen, put into freezer bags. you can do the same with tomato sauce. 