For nearly 30 years, Jessica was in a relationship with playwright, actor and director, Sam Shepard. The pair first met on the set of the 1982 film, Frances, and went on to have a "tumultuous" relationship. 

Opening up about their romance during a 2010 interview with The Guardian, Sam said: "I mean, we have long periods of relative calm. But then you know…"

"We're definitely an incredible match," he continued. "But, you know, not without fireworks… although at this point, you know, she's the only woman I could live with. Who could live with me! What other woman would put up with me?"

Sam sadly died of complications from ALS in 2017 at the age of 73.

Prior to her relationship with Sam, Jessica was married to photographer Francisco "Paco" Grande. She also dated Latvian dancer and actor Mikhail Baryshnikov, with whom she had her first daughter in Shura in 1981.

Jessica's first child, Alexandra Baryshnikov, was born in 1981 from her relationship with renowned ballet dancer Mikhail Baryshnikov. 

Alexandra, who goes by Shura, followed in her parents' footsteps in pursuing a career in dance and acting. 

She went on to attend Marlboro College in Vermont and is now the head of Movement at the Brown University/Trinity Repertory Company MFA Program in Acting and Dancing.

Speaking about her daughter during an interview with Vanity Fair, Jessica said: "Shura has a great sense of herself," adding that she's always been "very grounded". 

Meanwhile, Shura described her parents as "hugely inspiring individuals".

"The way we lived was inspiring," she told South Coast Today. "We were always surrounded by creative people. It’s part of the fabric of who I am whether conscious of it or not."

Jessica shares her second daughter, Hannah, with Sam Shepard. 

Hannah, who was born in 1985, has largely stayed out of the public eye.

During a 1991 interview with Vanity Fair, Jessica described her then-five-year-old daughter as a "powerful personality."

In 1987, Jessica and Sam welcomed their second child, Samuel Walker Shepard, who goes by Walker. Like his parents, Samuel carved out a career in the entertainment industry and plays the fiddle, guitar, banjo and harmonica for the band The Down Hill Strugglers.

While discussing their chosen careers, Jessica previously told People: "I love the fact that they've found their own way, and found their own passion."