Duncan, at an elevation of 3,535 feet, is astride the Gila River in southern Greenlee County. A few miles from Arizona's border with New Mexico, the town is 166 miles northeast of Tucson and 204 miles southeast of Phoenix. Originally known as Purdy, the name was changed to Duncan with the arrival of the old Arizona and New Mexico Railroad in the early1880s. Some sources say the settlement was renamed for James Duncan, a director of the Arizona Copper Company, in 1883.Another writer said the rail stop, which was a cattle-shipping point, was on property owned by Duncan Smith. The city incorporated in 1938. In its territorial days, it was said to have been known as a “tough town” that served as a watering point for notorious bad men, among them stagecoach and express robber “Black Jack” Ketchem and his gang.


Duncan is in the heart of Greenlee County's principal agricultural area, the verdant and fertile Duncan Valley. Some 10,000 acres are under irrigation and produce about 5,000 bales of cotton annually. Other crops are grains, potatoes, melons and chili. Cattle continue to play an important role in the economy, both on dairy farms and on cattle ranches. The commercial sector consists of small retail and service establishments that meet community needs and those of the surrounding agricultural area. The county's principal economic activity centers on the Phelps Dodge Corporation's copper mining operation 32 miles north of Duncan in the Clifton-Morenci area. Mining operations account for more than 50 percent of total county employment. Significant natural resources in the area include copper, molybdenum and zinc.


Near Duncan on the Lazy B Ranch is the largest fire-agate field in the nation. The surrounding hills are covered with geodes and other rocks to satisfy the most avid rockbound. Indian writings and other artifacts can be found by the hiker in many of the box canyons and cliffs in the area. The Lazy B Ranch was the childhood home of Sandra Day O'Connor, the first woman appointed to the U.S. Supreme Court. To the west of Duncan is Swift Trail, cutting a path through the Pinaleno Mountains capped by Mount Graham with an elevation of 10,700 feet. North is the scenic Coronado Trail through the mountainside valleys of the Apache National Forest. Also of interest to the north are the open pit mines in Morenci and historic Chase Creek in Clifton. Hunting in the area includes turkey, bear, mountain lion, deer and javalina. Catfish are plentiful in the waters of the Gila River.