Hats and Bonnets
Until the 20th century women always wore something on their heads. In 19th-century America and England, they would usually have worn bonnets, and occasionally hats.
Bonnets generally were made from soft material, tied under the chin, did not cover the forehead, and did not have brims (though fancier ones could). They were worn for warmth or shade, and to protect from dust. They could be very plain, such as those worn by Quakers:
Or they could be elaborately trimmed:
Hats were less common than bonnets and were worn for special occasions - to church or weddings. They had more structure than bonnets and were often made from straw, with wide brims and flat crowns, trimmed with flowers, feathers and other shapes. They were usually worn across the forehead.
For more bonnets and hats of the era, see these Pinterest boards: