When did it come into vogue for women to shave their legs and underarms?

U.S. women were browbeaten into shaving underarm hair by a sustained marketing assault that began in 1915. (Leg hair came later.) The aim of what Hope calls the Great Underarm Campaign was to inform American womanhood of a problem that till then it didn't know it had, namely unsightly underarm hair.

To be sure, women had been concerned about the appearance of their hair since time immemorial, but (sensibly) only the stuff you could see. Prior to World War I this meant scalp and, for an unlucky few, facial hair. Around 1915, however, sleeveless dresses became popular, opening up a whole new field of female vulnerability for marketers to exploit.