Corsets reached the height of their popularity during the Victorian era, worn by both men and women, only to be displaced in the 20th century by the mass production of a different kind of support garment and a world war.
Although the brassiere has its origins in the ancient world, it wasn't until 1914 that a design created and patented by Mary Phelps Jacob would gain widespread usage and acceptance. Lightweight and comfortable, Jacob's "Backless Brassiere" separated each asset rather than pushing them together as with a corset. In the 1920s, individual cup sizes would follow, allowing for a more comfortable garment.
World War I wasn't just fought on the battlefield every day. It was also a struggle in the underwear drawers of women across America. The U.S. War Department asked women to stop buying corsets, in order to use those materials for the war effort. The campaign proved successful, saving enough steel to build two battleships.