Cothran will step down from the position she held since 2007.
Warren, who co-founded the theatre in 1988, will depart at the end of the year.
Shields will leave a post at New Jersey’s McCarter Theatre Center and begin in San Diego in October.
The Atlanta native will take the reins as managing director, replacing Jenn Dwyer-McEwen.
Michael Menendian and JoAnn Montemurro will step down from the Chicago theatre after 35 years.
New York magazine’s new critic is also New York’s newest critic, and she says she’s as ready to listen as to talk.
She leaves after nine years at the Colorado company, where she oversaw growth in new-play and education programs.
A theatremaker and director, Holdren succeeds Jesse Green at the magazine starting July 31.
Raymond Bobgan, Will Davis, Jamie Herlich, Benita Hofstetter Koman, Johnny Morales, and Randy Reyes join the national theatre organization’s leadership.
After nine years with the Altanta company, she’s taken a culture post with the city of Hilton Head.