Under their leadership, CTH has become an internationally recognized organization. Its productions have received 13 AUDELCO Awards, six OBIE Awards, two Lucille Lortel Awards, a Drama Desk Award, and an Edwin Booth Award for Outstanding Contribution to New York Theatre, among other honors.

For CTH, McElroen directed such productions as The Cherry Orchard with Wendell Pierce and Earle Hyman, Jean Genet's The Blacks: A Clown Show and Waiting For Godot, which has toured widely. Preisser's directorial credits for the company include original adaptations of Medea, The Trojan Women, Nobel-prize winner Derek Walcott's Dream on Monkey Mountain, Electra, and King Lear, which went on to open the 75th Anniversary Season of The Folger Shakespeare Theatre in Washington D.C.