We attempt to catalogue those features of the three-dimensional structure of the Earth that are well-constrained by low-frequency data (i.e. periods longer than about 125 seconds). The dominant signals in such data are the surface-wave equivalent modes whose phase characteristics are mainly affected by a large scale structure of harmonic degree two in the upper mantle. Available aspherical models predict this phase behaviour quite well, but do not give an accurate prediction of the observed waveforms and we must appeal to higher-order structure and/or coupling effects to give the observed complexity of the data. Strong splitting of modes which sample the cores of the Earth is also observed and, though we do not yet have a model of aspherical structure which gives quantitative agreement with these data, anisotropy or large-scale aspherical structure in the inner core appears to be required to model the observed signal.