According to Life magazine, in 1889 Herminie Cadolle of France invented the first modern bra. It appeared in a corset catalogue as a two-piece undergarment, which she originally called the corselet gorge, and later le bien-être (or "the well-being").
What did they use before bras?
Early bras were either wrap-around bodices or boned, close-fitting camisoles (both worn over the corset). They were designed to hold the bust in and down against the corset, which provided upward support.