We provide a historical review and critique of regional geoid and quasigeoid modelling over the Australian continent, covering the earliest models from the late 1960s through to the present day and beyond. The most recently released official model for GPS/GNSS surveyors, AUSGeoid2020, was specifically calculated to enable them to determine Australian Height Datum heights from Geocentric Datum of Australia 2020 ellipsoidal heights in a more direct manner without the need for postsurveying adjustments. We summarise the deficiencies in the Australian Height Datum and how they are now being addressed by a proposed new vertical height system that is underpinned by a gravimetric-only quasigeoid model. We also summarise the results of some experiments that we have conducted to explore potential refinements that could be made to our computational processes, and future plans to acquire gravity data in the problematic coastal zones using airborne methods.