A strapless dress is a garment that stays put around the upper body without shoulder straps or other visible means of support. The modern strapless dress first appeared in the 1930s, where it was popularised by designers such as Mainbocher, and, from the late 1940s, Christian Dior.
The July 18, 1938 issue of Life claimed that the 'absolutely strapless, sleeveless evening dress' was a 1937/38 invention. However, that was predated in 1932 by the actress Libby Holman (photo above), who had been photographed in an apparently strapless dress that year. Holman became associated with the strapless dress and is regularly credited with inventing it, or at least being one of its first high profile wearers.