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The leek is a vegetable, a cultivar of Allium ampeloprasum, the broadleaf wild leek. The edible part of the plant is a bundle of leaf sheaths that is sometimes erroneously called a stem or stalk. The genus Allium also contains the onion, garlic, shallot, scallion, chive, and Chinese onion.

Historically, many scientific names were used for leeks, but they are now all treated as cultivars of A. ampeloprasum. The name 'leek' developed from the Anglo-Saxon word leac. Two closely related vegetables, elephant garlic and kurrat, are also cultivars of A. ampeloprasum, although different in their uses as food.