Girdles : the 20^th Century descendant of the corset, beginning in the 1920s. Girdles have progressed from boned ,open end control garments of coutil to lightweight elastic roll ons with or without legs. One distinguishing feature is that the girdle confines the body below the waist. Their function was to both smooth and control the body and hold up stocking through attached garters/suspenders. Their hey day was the 1930s - 50s. As the looser, freer fashions of the 60s took hold, and as both pants and pantyhose made great gains with the public, girdles faded in popularity. The girdles practical successors seem to be the decorative garter belt for those who prefer stockings, and the all un-boned Lycra smoother/shaper undergarments, often without garters. Styles include the long or short open elastic roll on girdle, panty girdles in satin or elastic stretch, and long line girdles that come down on the thigh . " Foundation garment" usually refers to an all-in-one that combines the bra and the girdle, again either open bottom or panty style.

Rollover (or open end) girdle late 40's early 50s
Courtesy of alonesolo/fashiontales

70's Girdle: Sturdy high waist style with hook and eye closures covered by a nylon zipper with stretchy white lace with a raised floral design,shimmery lace ruffles at the leg openings and cotton gusset 
Courtesy of late*bloomers

Sheer Vintage Girdle with metal hardware, small tummy insert and open bottom
Courtesy of bartondoll