Grenier's mother, who was an announcer on a Polish radio program, met his father when he was working as a sound engineer at WBNX in the Bronx in the late 1930s.

In 2010, he was cast on the television series The Good Wife as David Lee, a senior attorney, a role that soon became part of the recurring ensemble.

Notably, he played Edward Norton's boss in Fight Club and Mel Nicolai in Zodiac, both David Fincher films.

He appeared in the 1988 film Talk Radio as finance guru Sid Greenberg, a role he played in the original stage version of the script.

In 2009, he appeared on Broadway opposite Jane Fonda in 33 Variations,[5] earning him a Tony Award nomination.