The most wearable hats for contemporary life are those that can be squashed into a bag and not lose their shape. Soft buckets and turbans fit the bill, and there are many on the runways that inspire. Last season’s bucket evolves with a variety of brim widths, from narrow bands to eye-covering styles that are deeper at the back for full sun-protection. Materials include sturdy twills in solids or prints, lizard effects and lustrous jacquards. Trapunto stitches or contrast facing provide a bit of structure.