Duncan was founded in the mid-19th century, and the land was added to the United States as a part of the Mexican Cession, and the Gadsden Purchase.

Surrounding smaller unincorporated settlements such as Franklin and York in Arizona, and the Village of Virden, New Mexico, all use Duncan public schools.

caused them to vanish, (a remnant of the Chiricahua Band of Apache Indians remained in the upper Gila River Valley as late as the 1930s) as well as artifacts from garrison camps of the expedition of Francisco Vázquez de Coronado.

Duncan High School (mascot: Wildkat; school colors: red, grey, and white) competes in many sports, Fall- Mens "8 Man" Football AIA Div 1, Ladies VolleyBall, M/W Cross-country; Winter - M/W Basketball; Spring - Mens Baseball, Womens Softball, M/W Tennis, M/W Golf, M/W Track & Field.

U.S. Supreme Court Justice Sandra Day O'Connor was born in El Paso, Texas, but grew up near Duncan on the Lazy B ranch, which straddles the border between Arizona and New Mexico.

According to the United States Census Bureau, the town of Duncan has a total area of 2.2 square miles (5.6 km2), all of it land.

In April the average diurnal range is as high as 43.7 °F (24.3 °C) and it is only less than 36 °F (20 °C) in the often stormy months of July and August when over a third of the year's total rainfall can be expected.

Rainfall is generally scanty outside of the monsoon season, with substantial falls from winter storms being rare, although December 1991 did see 4.76 inches or 120.9 millimetres of rain.