Zelda was born to Marsha Garces Williams, the second wife of Robin Williams. The first of Marsha's two children, Zelda has an older half-sibling from Robin's first marriage, Zachary Pym (born April 11, 1983), as well as a younger brother Cody Alan (born November 25, 1991). The family currently resides in San Francisco.
Zelda has been quoted as saying she plays "every single sport on the face of the planet. I'm such an active person that without that, I think I'd just go crazy with energy." She regularly visits an indoor climbing gym in her hometown of San Francisco. Zelda is also a dedicated video game player and stated that Wikipedia is one of websites she frequently visits.
Zelda's acting debut was in the 2004 film House of D opposite Anton Yelchin as his young first love, Melissa Loggia. In House of D, she worked alongside her father, Co-star Robin Williams. Though the film was given mixed reviews, Zelda, along with cast-mate Anton, were well received. She filmed in Chicago in 2007 on the independent film "Were the World Mine", and has recently begun shooting Horror film "Don't Look Up" in Los Angeles.