The stadium is named for Ralph "Shug" Jordan, who owns the most wins in school history as a head coach, and Cliff Hare, a member of Auburn's first football team as well as Dean of the Auburn University School of Chemistry and President of the Southern Conference.

For years, it has been a fixture on lists of the best collegiate gameday atmospheres and one of the most intimidating places for visiting teams to play.

[4][5][6] Before 1939, Auburn played its home games under Coach Jack Meagher at Drake Field, a bare-bones facility seating only 700 people in temporary bleachers.

Head coach, Jack Meagher, was a driving force to raising funds and building a permanent stadium at Auburn.

[7] While the school was officially known as Alabama Polytechnic Institute until 1960, it had been popularly known as "Auburn" for years, and the decision to name the stadium as such reflected this.

The game was rescheduled in order for the stadium to be dedicated on Thanksgiving Day, Auburn officials seemingly wanting the significance of the occasion to dovetail with America's established Thanksgiving Day football tradition, a plan nearly thwarted by Franklin D. Roosevelt's "Franksgiving" decree.

The yearly Iron Bowl clash between Alabama and Auburn had been played at Legion Field since it was renewed on a permanent basis in 1948.

Initially, it made sense to play the Iron Bowl at Legion Field, since neither school's home stadium at the time had nearly enough seats to accommodate the crowds attending the game.

From the 1970s onward, however, Auburn fans increasingly felt chagrin at facing Alabama in Birmingham, particularly after the 1980s expansions allowed Jordan-Hare's capacity to eclipse that of Legion Field by over 2,000 seats.

By the time Dye became head coach and athletic director at Auburn in 1981, calls to make the Iron Bowl a home-and-home series had grown to a fever pitch.

In 1998, artist Michael Taylor was commissioned to paint ten large murals on the east-side exterior of the stadium.

Before the 2007 season, a $2.9 million, 30-foot (9.1 m) high by 74-foot (23 m) wide HD Daktronics LED video display was installed in the south end zone of Jordan–Hare Stadium.

Auburn was the first Southeastern Conference school to install an HD video display and the second in the NCAA (after Texas' Godzillatron).

In 2015, Auburn considered a complete reconstruction of the north end-zone section, which would have included new premium club seating and lounges, as well as establishing a new home locker room to replace the existing facility in the south end zone.

[19] After surveying donors and the fan base at large, the university did not move forward with those plans, deciding instead to build a $28 million gameday support facility in the southwest corner of the stadium.

The project includes renovation and expansion of the existing home locker room, relocation of the press box, a new player recruiting lounge, and a new premium fan club providing overviews of the end of Tiger Walk.

However, in June 2024, the AHSAA announced its football championship games would no longer be played at Jordan-Hare or Bryant-Denny stadiums, citing the expanded format of the College Football Playoff that could potentially see either school host a first-round playoff game in December.