It is located approximately 4 km (2.5 mi) south-east of the Adelaide city centre in the suburb of Glenunga, between L'Estrange and Conyngham Streets, adjoining the major thoroughfare Glen Osmond Road.

It adopted its current name upon the introduction of the International Baccalaureate Diploma Programme in 1990–91 with the aid of The Honourable Greg Crafter,[5] a development which was instigated to help save the school from closure due to dwindling student numbers.

With enrolments rising, GIHS has subsequently attracted substantial government funding and construction projects, most notably the technology and science wing extensions, a new administration block, and a performing arts centre; since 2005 there have been various additional changes to the facilities, such as extra rooms.

[9] As of 2015, Glenunga has over 50 student-led clubs, which include Literature, Musical Theatre, Debating, Chess, Science, Film and Raspberry Pi, amongst others.

This includes the Learner, International Mindedness, and Wellbeing Councils, student driven bodies who co-ordinate events and a number of other responsibilities.