Taylor's play Magnolia, set during the beginning of desegregation in Atlanta in 1963, premiered at Chicago's Goodman Theatre in March 2009 directed by Anna Shapiro. after receiving a workshop production in July 2008 at the National Playwrights' Conference at the Eugene O'Neill Theater Center in Waterford, Connecticut.

Taylor was born in Dallas, Texas. Her mother, Nell Taylor, is a social worker and poet. At age twelve, she moved to Muskogee, Oklahoma. The family later returned to Dallas, where she graduated from L. G. Pinkston High School in 1977.

Her earliest professional acting roles were two made-for-television films while she was studying at Southern Methodist University: 1980's Nurse and 1981's Crisis at Central High. In the latter movie, she was praised by critic John O'Connor of The New York Times for her portrayal of Minnijean Brown, a member of the Little Rock Nine, a group of African-American students who braved violence and armed guards to integrate Little Rock Central High School in 1957. Her first role to gain widespread attention was that of Mrs. Carter, the drug-addicted mother of a promising young female student, in the 1989 film Lean on Me. She became well-known to the television viewing public for her role as Lilly Harper on the early 1990s TV series I'll Fly Away. This role won her a Golden Globe award for Best Actress in a Television Drama and also an NAACP Image Award for Outstanding Actress in a Drama Series.

She wrote Escape From Paradise, a one-woman show which was produced at the Goodman Theatre Studio, Chicago, in October 1995. Her short plays Watermelon Rinds and Inside the Belly of the Beast were incorporated into a program at the Goodman Theatre Studio in 1994. Her other plays include Mudtracks, Love Poem #97 and Love Poem #98.

Taylor is also an accomplished stage Actress, and was the first black woman to play Juliet in Romeo and Juliet on Broadway. Her other Broadway credits include Macbeth and As You Like It. She appeared in Off-Broadway and regional productions of such plays as Jar the Floor (Off-Broadway, 1999), Machinal (Off-Broadway, 1990), L'Illusion (Off-Broadway, 1988), and A Map of the World (Off-Broadway, Public Theatre). She appeared as "Ariel" in The Tempest at the La Jolla Playhouse, California in 1987, for which she received a Dramalogue Award.

She wrote and appeared in the play Millennium Mambo, a one-woman work, presented at the Goodman Theatre in February 2000. The work also included short pieces by playwrights Adrienne Kennedy, Ntozake Shange, Suzan-Lori Parks and Kia Corthron. She wrote the play A Night in Tunisia, which premiered during the 2000 Alabama Shakespeare Festival. In 2000, Taylor won a best new play award from the American Critics' Association for Oo-Bla-Dee, a play about 1940s female jazz Musicians. The Goodman Theatre produced the play in 1999.

She wrote and directed Crowns, which is a co-production of the McCarter Theatre, where it premiered in October 2002 and the Second Stage Theatre, produced in December 2002. Crowns is described by Playbill as a "play-with-gospel-music", and is based on the book of the same name of photographs by Michael Cunningham and Journalist Craig Marberry.Crowns has been produced in various locations, including the Meroney Theater in Salisbury, North Carolina with The Piedmont Players in May 2009; the Zach Theatre in Austin, Texas in September 2004, the Pasadena Playhouse in co-production with Ebony Repertory Theatre in July 2009; Syracuse Stage in Syracuse, New York; at the Connecticut Repertory Theatre in Storrs, Connecticut in May 2009 and at the Electric City Playhouse in Anderson, SC in May 2011. Crowns was the most performed musical in the country in 2006. It won four Helen Hayes awards (for Washington, D.C. productions), including Taylor’s win for Best Direction as well as Best Regional Musical.

She wrote and directed an adaptation of Anton Chekhov's The Seagull titled Drowning Crow. Drowning Crow was produced on Broadway in February 2004 by the Manhattan Theatre Club at the Biltmore Theatre, directed by Marion McClinton.

She wrote and directed The Dreams of Sarah Breedlove, a dramatic rendering of the financial gains and emotional losses of African-American businesswoman Madam C.J. Walker, which received its world premiere production in January 2005 at the Alabama Shakespeare Festival.

Taylor returned to the Goodman Theatre in January and February 2011 for the world premiere of her new play entitled The Trinity River Plays, a co-production with Dallas Theater Center, directed by Ethan McSweeny. The production is a trilogy composed of Jar Fly, Rain, and Ghoststory.

Taylor is currently the writer-in-residence at the Signature Theatre, where her new play stop.reset. premiered at the Off-Broadway Pershing Square Signature Center on September 8, 2013. Taylor also directed the production.

Since then she has had some critical success for various supporting roles in films, such as the Spike Lee film Clockers, Courage Under Fire, A Family Thing, The Negotiator, and for the films Losing Isaiah and Strange Justice — a Showtime original film in which she portrayed Anita Hill — and as the lead in the PBS telefilm Cora Unashamed, based on a Langston Hughes short story. She was a cast member for all four seasons of the CBS drama The Unit as Molly Blane, the tough-minded housewife who holds the women of "the Unit" together when their husbands are on covert assignments.

In 2016, Taylor starred in the original pilot of Time After Time as Vanessa Anders, but was replaced by Nicole Ari Parker before the series aired, containing a new pilot with Parker.