Yu grew up in Los Altos Hills, California. Her father, Dr. John Kou-ping Yu, an oncologist, was born in Shanghai. Her mother, Connie Young Yu, writer and historian, is a third-generation Californian.^{[citation needed]}

Yu graduated from Gunn High School in Palo Alto.^[when?] She was a reporter for the school newspaper, The Oracle.^[3]

She went on to attend Yale University, where she was a two-time NCAA All-American and three-time All-Ivy in fencing.^[4] As a world-class foilist, she was a member of the Junior World Team and the United States national team at the World Championships and World University Games.^{[citation needed]} Yu graduated from Yale University in 1987^[5] summa cum laude, Phi Beta Kappa,^[6] with a bachelor's degree in English.^[7]

After graduation, Yu thought of pursuing law school like her peers. However, her father discouraged her from doing so.^[8] She discovered film production while searching for a job that allowed flexible hours to allow her to compete in fencing. She started as a production assistant in 1989^[4] on a few commercials, where she got to arrange frozen noodles on forks and re-park cars. When she started working in documentary, she became further intrigued by the process.^[9] Yu refused to attend film school and gained her film education on the job. She focuses on making documentaries but says that one day she'd love to make a fully animated comedy feature.^[9] The opportunity to make film is a random occurrence for Yu.^[10] Her documentary films present worldwide issues that people face every day and allow the subjects to speak for themselves as much as possible. She is adamant that story should come before politics.^[1] Her films intend to inform the general public to incite people to become active in everyday issues such as water conservation and regulation.^[11] When not making documentaries and feature films, Yu spends time directing television shows.

Yu began her career in 1993 with her short Sour Death Balls, a silent black-and-white montage of assorted subjects' reactions to blindingly bitter candy, which was shot on an old school Bell & Howell wind-up camera.^[1] She got her inspirations from daily interactions in her life, i.e. when a child offered local people sour candy. Yu sent the short film to film festivals, and it became her first feature at the Telluride Film Festival in 1993.^[12] Yu made her first documentary, Men of Reenaction (1994), which explores the extremes of people searching for authenticity through Civil War reenacting.^[13]

Her most famous work was her Academy Award-winning Breathing Lessons: The Life and Work of Mark O’Brien. The documentary short features Berkeley writer Mark O'Brien, a disabled poet with an iron lung. His editor at the Pacific News Service, Sandy Close, introduced the pair and suggested that a film be made.^[8][14] It debuted at the 1996 Sundance Film Festival and won several honors, including the International Documentary Association Achievement Award for Best Documentary, before the Academy Awards.^[4]

Yu's 1998 HBO documentary The Living Museum, which follows Creedmoor Psychiatric Center patient Issa Ibrahim, was nominated for the Grand Jury Prize at the 1999 Sundance Film Festival.^[15]

In the 2000s, Yu's chance to work in episodic TV came when she received an invitation to apprentice at John Wells Productions as the first participant of their director diversity program. Shadowing directors, Yu sensed she was a guinea pig. “If you screw this up,” she told herself, “they’ll never let another woman of color from documentaries do this again.”^[1] While working for Wells' production company, she began directing in television for shows like Grey's Anatomy and The West Wing.^[4] On her first directorial assignment, an episode of The West Wing, Yu was heartened that Wells encouraged her stylistic input. “He made a point of saying, ‘You should bring your own ideas to the table,’ rather than just follow prescribed formula.” So she decided to open with a series of mood-establishing low, wide-angle shots to signal the calm before the gathering storm.^[1]

She directed a sport comedy film, Ping Pong Playa (2007), that explored Asian family culture through a Chinese ping pong playing son that is trying to prove himself to his family. Her producer friends Joan Huang and Jeff Guo approached her with the idea of working on a comedy together. They felt the time was right to have an obnoxious Asian American character on the screen. Yu and her comrades felt that Asian American cinema had plenty of good dramas and wanted to fill the void of superficial comedy.^[9] She tried to bring the same loose hand and adaptability she used for documentaries to scripted material. Her approach to Ping Pong Playa was to “have a lighter touch, especially with actors” to give them a sense of freedom.^[1]

In her later documentaries such as Last Call at The Oasis (2011) and Misconception (2014), Yu focused on capturing the big picture and understanding how these issues intertwined with other aspects of life such as climate, population, and the environment.^[16] Last Call at The Oasis addresses the water crisis in the United States, and working on the film made her consider the impact of the crisis on her children and their children. This project became more personal to Yu and compelled her to complete it. It took six months of research prior to filming, as Yu wanted to create the big picture of the facts and threats of the water crisis in the domestic United States.

Last Call at the Oasis inspired Yu to direct her 2014 documentary Misconception, which paints the population issues from a person-to-person point of view. While filming Last Call at the Oasis people questioned the purpose of acting on water conservation because they cannot control the population growth affecting it. Her main goal is to take this topic and tie with emotionally, entertaining, and interesting stories.^[17]

The majority of her work after 2015 has been focused on television production and directing. For Netflix, she directed episodes of the dramas 13 Reasons Why and Hollywood and did Maria Bamford's comedy special Old Baby.

Jessica's work in the 2020s includes directing a number of television drama series. This Is Us (Don't Let Me Keep You, 2021), The Morning Show (Kill the Fatted Calf, 2021), In Treatment (Brooke, Laila, Colins, Eladio, 2021).

Yu is married to author Mark Salzman. They and their daughters, Ava and Esme, live in Los Angeles.^{[citation needed]}

Jessica has an older sister, Jennifer Yu, a technical publications manager, and a younger brother, Martin Yu, an actor.^[18]