According to theater scholar and critic Melissa Sihra, Carr's plays have been produced in award-winning productions at the Abbey, Peacock, Gate, and Project Theatres in Dublin as well as the San Jose Repertory Theatre, Irish Repertory of Chicago, the Pittsburgh Irish and Classical Theatre, and the MacArthur Theatre at Princeton in the United States.
By the Bog of Cats premiered at Dublin's Abbey Theatre on Wednesday, October 7, 1998 and ran for 45 performances until Saturday, November 14, 1998. Actress Olwen Fouere created the role of Hester Swane.
The American premiere was staged by Irish Repertory of Chicago, opening May 31, 2001. Carr made several script changes for this production, mostly having to do with the Joseph Swane scene in Act III. The production was directed by Kay Martinovich, and featured Tracy Michelle Arnold as Hester, along with Mark Montgomery, Mary Ann Thebus, and David Darlow in the principal roles. Critical reception was strongly positive, with Chicago Sun-Times critic Hedy Weiss writing "...the play is now receiving a riveting, brilliantly acted American premiere by Irish Repertory, in a production superbly directed-with chilling inevitability and unexpected humour-by Kay Martinovich."
The 2004 West End revival of By the Bog of Cats starred Holly Hunter. Reviews of this production were mixed. While most reviewers praised Hunter's performance, many found issues with the play itself. Matt Wolf, in a review for Variety, decries the "blarney in which 'Bog' is bogged down." Charles Spencer, in a scathing article for the Telegraph, states that Marina Carr "delivers little more than a ludicrously rich stew of over-heated tosh" in By the Bog of Cats.  Alan Bird, writing for London Theatre, differs in calling By the Bog of Cats "an outstanding dark psychological drama" and a "hilarious dark comedy."
By the Bog of Cats returned to Dublin's Abbey Theatre from August–September 2015. Elements of this production were slightly satirical. For example, the Ghost Fancier was depicted as a "singing cowboy" who is "trailed by country and western music." Additionally, reviewer Peter Crawley connects the Kilbride family to the newly rich Irish at "the crude beginnings of the Celtic Tiger years." Crawley had several criticisms for the play, including finding Hester a less than interesting character and calling the second act "structurally unwieldy." 
A recent production of By the Bog of Cats premiered at Chicago's Artistic Home Theater on February 15 and ran through April 15. The production received a rating of 3 stars from reviewer Kerry Reid. Reid noted that Carr's plays are produced "stateside far less" than other Irish playwrights, despite a "long-running relationship with Dublin's celebrated Abbey Theatre, which has served as a pipeline for Irish dramatists to American stages for decades."  Reid contends that the play has not been produced locally since the defunct Irish Repertory of Chicago produced it in 2001.