- Won 2008 Best Actress Tony Award for her role as Violet in "August: Osage County.".
- Nominated for a Tony for her role in Tracy Letts's play "August: Osage County", which premiered at the Steppenwolf Theatre in Chicago, where Dunagan is a regular.
- She has English, Irish, Scottish, Welsh, and German ancestry.
- She was nominated for a 1989 Joseph Jefferson Award for Actress in a Supporting Role for "Stepping Out" at the Steppenwolf Theatre Company in Chicago, Illinois.
- She was nominated for a 1991 Joseph Jefferson Award for Actress in a Principal Role in a Play for "Coriolanus" at the Next Theatre Company in Chicago, Illinois.
- She was nominated for a 1991 Joseph Jefferson Award for Actress in a Supporting Role in a Play for "Still Waters" at the Victory Gardens Theater in Chicago, Illinois.
- She was nominated for a 1992 Joseph Jefferson Award for Actress in a Supporting Role for "Private Passage" at the Odyssey Theatre in Chicago, Illinois.
- She was nominated for a 2002 Joseph Jefferson Award for Actress in a Supporting Role in a Play for "A Lie of the Mind" at the American Theater Company in Chicago, Illinois.
- She was awarded the 2003 Joseph Jefferson Award for Actress in a Supporting Role in a Musical for "James Joyce's The Dead" at the Court Theatre in Chicago, Illinois.
- She was awarded the 2004 Joseph Jefferson Award for Actress in a Supporting Role in a Play for "I Never Sang for My Father" at the Steppenwolf Theatre Company in Chicago, Illinois.
- She was awarded the 2007 Joseph Jefferson Award for Actress in a Principal Role in a Play for "August: Osage County" at the Steppenwolf Theatre Company in Chicago, Illinois.
- She was nominated for a 2016 Joseph Jefferson (Equity) Award for Actress in a Supporting Role in a Play for "Marvin's Room" at the Shattered Globe Theatre in Chicago, Illinois.
- She was nominated for a 2018 Joseph Jefferson Equity Award for Performer in a Supporting Role in a Play for "Blind Date" at the Goodman Theatre in Chicago, Illinois.
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