Fitted caps use to be only worn by baseball players and rather expensive and hard to find. These days anyone can find a fitted cap and they can be found almost anywhere. Fitted caps are suitable for men, women and children. You can get a hat featuring almost anything imaginable and suitable for any occasion.
While fitted caps come in both custom sizes and general sizes the concept is the same. Custom sized caps are more expensive than the general sizes and may be harder to find. Today fitted caps are usually made with an elastic band that will stretch, if needed, to fit the wearers head. This allows the manufacturers to create an adult and youth version and mass produce fitted caps. Since they can be produced in large quantities they can be made and sold for cheap prices.
Men of any age can feel free to wear a fitted hat for most occasions and places except the obvious - evening and office. Many workplaces even allow them. They can be worn with the brims facing sideways, or tipped up. Or even the old-fashioned way. Basically, whatever feels right to you on a given day is fair game.