Greif is best known for directing musicals such as Grey Gardens and Rent, but his extensive resume includes an array of plays with varied styles and content. His Public Theater credits include Diana Son's Satellites, Suzan-Lori Parks' Fucking A, Jessica Hagedorn's Dogeaters, Jose Rivera's Marisol, Pericles, Connie Congdon's Casanova, Tony Kushner's A Bright Room Called Day and Sophie Treadwell's Machinal. Greif has also directed at most of New York's leading nonprofit theaters Roundabout, Signature, Playwrights Horizons, MCC, Manhattan Theatre Club and New York Theatre Workshop, where is he an artistic associate. His Grey Gardens bio does not list any Shakespeare productions.