Greiman first studied graphic design in her undergraduate education at the Kansas City Art Institute, from 1966–1970. She then went on to study at the Allgemeine Künstgewerberschule Basel, now known as the Basel School of Design (Schule für Gestaltung Basel) in Basel, Switzerland (1970–1971). As a student of Armin Hofmann and Wolfgang Weingart, she was influenced by the International Style and by Weingart's introduction to the style later known as New Wave, an aesthetic less reliant on Modernist heritage.
Greiman moved to Los Angeles in 1976, where she established the multi-disciplinary approach that extends into her current practice, Made in Space. During the 1970s, she rejected the belief among many contemporary designers that computers and digitalization would compromise the International Style; instead, she exploited pixelation and other digitization "errors" as integral parts of digital art, a position she has held throughout her career.
In 1982, Greiman became head of the design department at the California Institute of the Arts. In 1984, she lobbied successfully to change the department name to Visual Communications, as she felt the term “graphic design” would prove too limiting to future designers. In that year, she also became a student herself and investigated in greater depth the effects of technology on her own work. She then returned to full-time practice and acquired her first Macintosh computer. She would later take the Grand Prize in Mac World's First Macintosh Masters in Art Competition. An early adopter of this computer, Greiman produced an issue of Design Quarterly in 1986, notable in its development of graphic design. Entitled Does it make sense?, the edition was edited by Mildred Friedman and published by the Walker Art Center. "She re-imagined the magazine as a poster that folded out to almost three-by-six feet. It contained a life-size, MacVision-generated image of her outstretched naked body adorned with symbolic images and text— a provocative gesture, which emphatically countered the objective, rational and masculine tendencies of modernist design." Miracle Manor, a desert spa retreat owned with her husband, architect Michael Rotondi, is a showcase for her more recent three-dimensional design of space in natural landscapes.
In 1995, the U.S. Postal Service launched a stamp designed by Greiman to commemorate the Nineteenth Amendment to the United States Constitution (Women's Voting Rights). In 2006, the Pasadena Museum of California Art mounted a one-woman show of her digital photography entitled: Drive-by Shooting. She was also recently in the group show at Centre Georges Pompidou in Paris, in a major exhibition Elle@Centre Pompidou. In 2007, Greiman completed her largest ever work: a public mural, "Hand Holding a Bowl of Rice," spanning "seven stories of two building facades marking the entrance to the Wilshire Vermont Metro Station in Los Angeles."
Greiman currently teaches at Woodbury University, School of Architecture and the Southern California Institute of Architecture (SCI-Arc). She is a recipient of the American Institute of Graphic Arts Gold Medal for lifetime achievement. She has received 4 honorary doctorates: Kansas City Art Institute (2001); Lesley University, The Art Institute of Boston (2002); Academy of Art University (2003,) Art Center College of Design (2012.)