In order to investigate seismic structures beneath the Australian continent and slab geometry of subduction zones around the Australian plate, we construct a new radially anisotropic shear wavespeed model, namely AU21, by applying full-waveform inversion technique to three-component data from 248 regional earthquakes and recorded by 1,102 seismographic stations. Twenty one preconditioned conjugate gradient iterations are utilized to minimize discrepancies between observed and synthetic seismograms, resulting 32,655 body-wave (15-40 s) and 35,897 surface-wave (25-100 s) measurements in the final iteration. AU21 confirms the sharp contrast in shear wavespeed perturbations between the Phanerozoic eastern continental margin with the Precambrian western and central Australia, and this boundary is offset to the east of the Tasman Line. The lithosphere-asthenosphere boundary is about 250-300 km beneath central and western Australia. A unique weak radial anisotropy layer at 80-150 km is observed beneath the western Australian craton, which may be caused by dipping layers alignments or tilted symmetry axes of anisotropic minerals. Slow anomalies extending down to the uppermost lower mantle beneath east of New Guinea, the Tasman Island, and the Tasman Sea may suggest deep thermal activities beneath these regions, possibly contributing to the formation of the low wavespeed band along the eastern Australian margin. Furthermore, we observe that the Tonga slab is stagnant within the mantle transition zone, while the Kermadec slab penetrates through the 660-km discontinuity down to the lower mantle.