As of May 2015, Delta's checked baggage policy varies greatly depending on the route traveled and ticket type. The airline allows one carry-on bag and one personal item, with some restrictions.
Approved personal items include a laptop, a briefcase or items of similar or smaller size. Jackets, umbrellas, food, drink and assistive devices do not count as a personal item and are free. The carry-on bag size limit is 45 linear inches.
Generally, a checked bag of at least 50 pounds is free on international flights. On domestic flights, there is a fee unless the passenger is in first or business class or has Delta One status.