Numerous seismic studies, in particular using receiver functions and explosion seismology, have provided a detailed picture of the structure and thickness of the crust beneath the Iceland transverse ridge. We review the results and propose a structural model that is consistent with all the observations. The upper crust is typically 7 ± 1 km thick, heterogeneous and has high velocity gradients. The lower crust is typically 15–30 ± 5 km thick and begins where the velocity gradient decreases radically. This generally occurs at the Vp∼ 6.5 km s−1 level. A low-velocity zone ∼10 000 km2 in area and up to ∼15 km thick occupies the lower crust beneath central Iceland, and may represent a submerged, trapped oceanic microplate. The crust–mantle boundary is a transition zone ∼5 ± 3 km thick throughout which Vp increases progressively from ∼7.2 to ∼8.0 km s−1. It may be gradational or a zone of alternating high- and low-velocity layers. There is no seismic evidence for melt or exceptionally high temperatures in or near this zone. Isostasy indicates that the density contrast between the lower crust and the mantle is only ∼90 kg m−3 compared with ∼300 kg m−3 for normal oceanic crust, indicating compositional anomalies that are as yet not understood. The seismological crust is ∼30 km thick beneath the Greenland–Iceland and Iceland–Faeroe ridges, and eastern Iceland, ∼20 km beneath western Iceland, and ∼40 km thick beneath central Iceland. This pattern is not what is predicted for an eastward-migrating plume. Low attenuation and normal Vp/Vs ratios in the lower crust beneath central and southwestern Iceland, and normal uppermost mantle velocities in general, suggest that the crust and uppermost mantle are subsolidus and cooler than at equivalent depths beneath the East Pacific Rise. Seismic data from Iceland have historically been interpreted both in terms of thin–hot and thick–cold crust models, both of which have been cited as supporting the plume hypothesis. This suggests that the plume model for Iceland is an a priori assumption rather than a hypothesis subject to testing. The long-extinct Ontong–Java Plateau, northwest India and Paraná, Brazil large igneous provinces, beneath which mantle plumes are not expected, are all underlain by mantle low-velocity bodies similar to that beneath Iceland. A plume interpretation for the mantle anomaly beneath Iceland is thus not required.