He has won three Obie Awards and received five Tony Award nominations, for Rent, Grey Gardens, next to normal (sic), Dear Evan Hansen, and Hell's Kitchen.

He was the Artistic Director of the La Jolla Playhouse, LaJolla, California from 1994 to 1999.

[7] In August 2023, it was announced that his Chicago Shakespeare Theater production of The Notebook would transfer to Broadway in March 2024 and in September 2023, it was announced that he would transfer his Off-Broadway production of Days of Wine and Roses to Broadway in January 2024.

[8][9] Among his many directing credits Off-Broadway are Alicia Keys' autobiographical musical Hell's Kitchen,[10] Katori Hall's Our Lady of Kibeho, John Guare's Landscape of the Body and A Few Stout Individuals at Signature Theatre,[11] Beauty of the Father for the Manhattan Theatre Club,[12] the 2009 Playwrights Horizons production of Mrs. Sharp (with music and lyrics by Ryan Scott Oliver and starring Jane Krakowski), and Romeo and Juliet, The Winter's Tale, and The Tempest at the New York Shakespeare Festival at the Delacorte Theater (2007, 2010, 2015).

[13] Grief has two children, born through artificial insemination with a lesbian friend.