In 1994, former fashion entrepreneur Murray Moss who helped shape the surrounding Soho retail geography, opened Moss in a small former gallery space in Soho, with a determination to transform the public perception of industrial product design. The store quickly became internationally known for its product selection and presentation, with clients ranging from highly informed design professionals, to celebrities, students, and tourists with maps.

Moss has opened its Los Angeles shop in 2008 at the SLS Hotel at Beverly Hills.