We use GPS observations to investigate the magnitude and spatial distribution of vertical coseismic and postseismic deformation of the Australian continent and compare these with elastic and viscoelastic model outputs. We observe and model surface deformation in Australia caused by six recent large far-field events: 2004 Mw 8.1 Macquarie Ridge, 2004 Mw 9.3 Sumatra-Anderman, 2005 Mw 8.6 in northern Sumatra, the 2007 series of Mw 8.5 and 7.9 in southern Sumatra, two events in 2012 of Mw 8.6 and 8.2 in northern Sumatra, and the 2009 Mw 7.8 south of New Zealand. Observed vertical coseismic deformation reaches 3 mm, with the magnitude varying spatially and by earthquake in broad agreement with modelling of coseismic deformation. Postseismic deformation is observed in all three coordinate components at Australian GPS sites nearest to these earthquakes, with deformations reaching several mm/yr in the vertical over multiple years. In particular, the Sumatran sequence produces observed subsidence in north-western Australia of up to 4 mm/yr over 2004.9-2010.0 where predictions based on one-dimensional viscoelastic Earth models replicate the subsidence but underpredict the vertical rate by a factor of two. Across all earthquakes, the models often fit one or two coordinate components of the observations, but rarely all three. Unmodeled lateral rheological structure likely contributes to this given the difference between the oceanic location of the earthquakes and the Australian continental setting of the GPS sites. The magnitude and spatial extent of these coseismic and postseismic deformations warrant their consideration in future updates of the geodetic terrestrial reference frame.