There are many different types of bras for varying purposes that are based on your need (maternity bras, mastectomy bras, sports bras, training bras), your build (small breasts: padded bras, large breasts: full figure and minimizer bras, etc..), your style requirements (shelf bras, strapless bras, demi bras). Just picking one type of bra may not be the right thing to do. So, with that in mind I have included a brief listing of some of the bra types and their roles.
Built-in bras, sometimes known as shelf bras, are a supportive brassiere like structure on the inside of another garment, such as a swimsuit or tank top, which provides support for the bust without the need for a separate bra. In most such garments, these consist of a horizontal elasticated fabric strip, although some do have cups and underwires as with other bra types.
Full support bras are a type of bra designed to offer good support for the whole of the breasts, and as such are a typical, practical bra for everyday wear.
Mastectomy bras are designed so that a prosthesis may be held in place and are intended for women who have lost one or both breasts in mastectomy treatment for breast cancer.
Maternity bras are slightly different from nursing bras though the terms are sometimes used interchangeably. Maternity bras are designed such that they can be expanded to adjust as the breasts increase in size over the course of a pregnancy.
Minimizer bras are designed to de-emphasize the bust, in particular, of large-breasted women. Minimizers, by compressing and shaping the breasts, help to create the illusion of being a cup size or two smaller.
Nursing bras are designed to help make breastfeeding simpler by allowing for easy access to the nipple. Traditionally, nursing bras are made with flaps of fabric over the cup which can be unclasped and pulled down to access the breast. Even with the “flap” pulled down, the cup of the bra supports the breast. There are also no flap versions made of stretchable fabric which can pulled to the side when it is feeding time. Underwire versions of nursing bras are discouraged because they can constrict the breast and can cause either blocked ducts or mastitis though underwire versions are readily available.
Padded bras are simply bras with padding added inside the lining. They are designed to provide a fuller shape for small breasts and an alternative to bra stuffing, a practice among preteen and teen girls in which tissues, cotton balls, or socks are placed inside a bra to simulate larger breasts. Unlike push-up bras, however, most padded bras support the breasts but do not significantly lift them.
Peephole bras have cups which loosely cover the breasts, but holes around the nipples. These kinds of bras do not give the breasts much support, and are generally found in lingerie sets and intended for wearing in sexual situations.
Push-up bras, are structured so that the breasts are lifted and the cleavage emphasised. The best known brand of push up bra is the Wonderbra. Many push-up bras contain padding, typically made of foam or rubber, but some contain pads filled with water, an oil/water mixture, or gel.
Demi bras have lower cut cups, covering approximately half the breasts. These offer less support, but enable low cut garments to be worn without the bra being seen. Also known balconette. Demi bras may be designed to provide lift as a push-up bra does.
Shelf bras have a band, usually elastic, that goes across the entire front of the chest, beneath both breasts. These are often found built into camisoles. The term is also used interchangeably with built-in bra.
Sports bras or jogging bras are for women to wear during exercise. They are more sturdy in their construction than regular bras, and offer greater support for the chest, thus increasing comfort and reducing the chance of damage to the ligaments of the chest during high impact exercises such as jogging. They are usually made of a stretchable, absorbant fabric such as Lycra, and may be designed to draw perspiration away from the skin to reduce irritation. Many women, particularly those with large breasts, find sports bras essential for exercise, as breasts bouncing can cause pain and discomfort, as well as embarrassment. Some sports bras are meant to be worn as outerwear.
Strapless bras, with no shoulder straps are designed for wearing with clothes that reveal the shoulders, such as halterneck tops. Convertible bras have straps which may be detached and rearranged in different ways depending on the outfit. Alternatives to regular straps for strapless bras are beaded bra straps or clear plastic bra straps, that provide support and style.
T-shirt bras are designed without raised seams, so that a tight t-shirt may be worn without the bra being visible.
Training bras are for girls who have begun to develop breasts but have yet to develop enough to allow for a standard sized bra to fit properly. They are of simple construction and offer little, if any, support. Training bras were invented in the 1950s in response to the desire of adolescent and pre-adolescent girls to “fit in” amongst their more developed peers. Some observers believe that training bras serve no functional purpose, and are exploitative in that they allow entrepreneurs to benefit from, and even encourage, precocious sexuality in young girls.  Still, others recognize developing tissue as sensitive and, at times, in need of coverage in order to maintain comfort. It is also said that training bras help the growth of a young girl’s breasts, although there is no evidence to support this.
Bullet bras have a round tip in the end of each cup of the bra, hence the shape of the cup is similar to a bullet. Bullet bras were invented in the 1950’s.