Wicker
The type of baskets that reed is used for are most often referred to as "wicker" baskets, though another popular type of weaving known as "twining" is also a technique used in most wicker baskets.
Popular styles of wicker baskets are vast, but some of the more notable styles in the United States are Nantucket Baskets and Williamsburg Baskets. Nantucket Baskets are large and bulky while Williamsburg Baskets can be any size, so long as the two sides of the basket bow out slightly and get larger as it is weaved up.
Read more about this topic: Basket Weaving