Born to a Jewish family, Landis graduated from UCLA with an M.F.A. in costume design in 1975. She earned her Ph.D. in history of design from the Royal College of Art in London. She has created iconic costumes throughout her career, such as the fedora and jacket of Indiana Jones (Harrison Ford), the "college" sweatshirt worn by John "Bluto" Blutarsky (John Belushi), and Michael Jackson's red jacket in Thriller. In addition to many Drama-Logue Awards for her theater designs, she was nominated for an Academy Award in 1988 for Coming to America.
Landis has lectured widely on costume design and taught classes at the University of Southern California, the AFI Conservatory, and is a professor at the University of the Arts London. She was inducted as a Distinguished Alumna at the UCLA Department of Theater, Film and Television in 2005, and honored as a william Randolph Hearst Fellow at the University of Texas, Austin in 2006. In 2007, she served on the Cinefondation Jury at the 60th Cannes Film Festival. In 2009, Landis became the David C. Copley Chair and the Director of the David C. Copley Center of Costume Design at UCLA, School of Theater, Film & Television.
Landis spent five years researching and designing "Hollywood Costume," which opened on October 20, 2012 at the Victoria & Albert Museum in London. With one hundred and thirty iconic costumes loaned by sixty international archives and private Collectors, "Hollywood Costume" was universally well reviewed and broke records at the V&A. Over 265,000 visitors saw the show before it closed on January 27, 2013. Landis headed the curation team as Senior Curator, with Sir Christopher Frayling, Guest Curator and Keith Lodwick as V&A Curator. The exhibition was designed by the London firm of Casson-Mann and the score for the exhibition was composed by Julian Scott. The 2013-14 exhibition tour includes the Australian Center for the Moving Image in Melbourne, The Virginia Museum of Fine Arts in Richmond, and the Phoenix Art Museum in Arizona.