Which type of hats are these called?

The 'cloche hat' or simply a 'cloche' is a fitted, bell-shaped hat for women that was invented in 1908 by milliner Caroline Reboux. They were especially popular from about 1922 to 1933. Its name is derived from cloche, the French word for "bell".

During the early twentieth century, the popularity and influence of cloche hats was at its peak. Couture houses like Lanvin and Molyneux opened ateliers to join milliners in manufacturing hats that precisely matched their clothing designs.

Cloche hats were usually made of felt so that they conformed to the head, and were typically designed to be worn low on the forehead, with the wearer's eyes only slightly below the brim. In later years, a summer cloche might be made from sisal or straw. Cloches could also be made of beads or lace for evening wear, for cocktails, dancing or even for bridal wear.

The contemporaneous Art Deco style often influenced the outline of the brim or the style of seams. A cloche could be decorated with appliqués, embroidery, jeweled brooches, scarves, fans of feathers, or similar accents. By the end of the 1920s, it became fashionable to turn the brims on cloche hats upwards. This style remained prevalent until the cloche hat went out of fashion around 1933 or '34. They are still made and worn today but are rarer and often referred to as a 'retro' styling cap.