A relatively new term in lingerie, the t-shirt bra has cups so smooth that it can be worn without showing through tee shirts and other clingy knits. The cups will be seamless and often padded or lined to prevent nipple see-through. Most t-shirt bras are constructed of molded poly-blend materials.
For those who prefer cotton in their lingerie, there is a selection of t-shirt bras constructed with at least some cotton. But even bras with up to 90% cotton will also have spandex, lycra or something similar to help them hold their shape. The cotton t-shirt bras are soft and breathable, with natural moisture-wicking properties, but all the smoothness you need in a t-shirt bra.