An aspect of the Concord Jazz Quartet that distinguishes it from other jazz groups from the Pittsburgh region is that the group consists of artists from both the European classical and American jazz traditions. Vibraphonist Andy Reamer and bassist Jeff Grubbs are long time members of the Pittsburgh Symphony Orchestra—one of the finest orchestras in the world—while guitarist Eric Susoeff and drummer Thomas Wendt are veterans of Pittsburgh's historic and storied jazz scene. The quartet was founded by Reamer and Wendt in 2015 and began performing at James Street Tavern. 

The group relies on repertoire from the classic jazz and Great American Songbook canons but also specializes in some of the "Third Stream" Jazz of the 1950s, which combines European classical with American jazz. The group has presented programs of Third Stream composer John Lewis' music at City of Asylum's Alphabet City venue in Pittsburgh as part of the Off Minor Jazz series.