The present invention provides hats with attachment assemblies allowing them to be detachably secured to an article of clothing. In one example, the attachment assembly permits the hat to be detachably secured in an exterior-side out configuration to a belt of medium width worn around the wearer's waist, without requiring the hats to be inverted or reversed, and without any need for pockets, linings, zippers or the like. The hats may also be provided with retention members for holding the hats in a simple folded configuration when carried on the person. In such a configuration small personal items such as keys, loose change, mobile telephones may be carried in the retained, folded hat.