The legal dispute began in 2018 when the Scottish Parliament passed a bill designed to ensure gender balance on public sector boards.
For Women Scotland complained that ministers had included transgender people as part of the quotas in that law.
After several cases in the Scottish courts, the issue has been sent to the Supreme Court in London for a final ruling.
For Women Scotland has warned that if the court sides with the government, it would have implications for the running of single-sex spaces and services, such as hospital wards, prisons, refuges and support groups.
Transgender people have warned the case could erode the protections they have against discrimination in their reassigned gender.
