- She holds American and British citizenship.
- To manage her education and career, she began homeschooling, and graduated (1999).
- Mother, Linda (Ekstrom), is a musician, who plays blues and jazz professionally. Father, Ron Moss, manages jazz musicians.
- Studied ballet with Suzanne Farrell at the Kennedy Center in Washington, D.C.
- Her favorite character that she has played has been Robin Griffin in Top of the Lake (2013).
- She is a second cousin, once removed, of Swedish musician Björn Ulvaeus, of ABBA. Elisabeth's maternal great-grandmother, Judith Linnea Nilsson, was the sister of Bjorn's maternal grandmother, Eleonora Constantia Nilsson.
- Her father was from England. Her mother, who is American, is of half Swedish and half German and Austrian descent.
- Nominated for the 2019 Golden Globe Award in the Best Performance by an Actress in a Television Series - Drama category for her role as June Osborne in The Handmaid's Tale (2017), but lost to Sandra Oh for Killing Eve (2018).
- Nominated for the 2018 Emmy Award in the Lead Actress in a Drama Series category for her role as June Osborne in The Handmaid's Tale (2017), but lost to Claire Foy from The Crown (2016).
- Nominated for the 2015 Best Actress in a Play Tony Award for her performance in "The Heidi Chronicles". She lost the award to Helen Mirren for her performance in "The Audience".
- Her favourite films are: Annie Hall (1977), When Harry Met Sally... (1989), Sunset Boulevard (1950), Sweet Smell of Success (1957), and All About Eve (1950).
- The Invisible Man (2020) marks the second time Moss was in a project involving a man wearing an invisible suit. The first time being in Batman: The Animated Series (1992) in the episode See No Evil (1993) where Moss voiced a little girl who's estranged father wears an invisible suit to get closer to his her.
- Is a lifelong member of the Church of Scientology.
- Born on the same date as Anna Paquin and Lauren Miller Rogen.
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