The character of the crust-mantle transition beneath Iceland, a ridge-centred hotspot, is not well known despite a wealth of geophysical data including recent seismic refraction profiles. scattered observations of a 20-40-km-deep seismic reflector and Pn velocities of 7.7-8.0 km s-1, it has been concluded that the Icelandic crust is 20-40 km thick and solid, underlain by solid upper mantle. Receiver functions are sensitive to seismic velocity contrasts and, therefore, well suited to study the proposed Moho. Several receiver function studies have been conducted meanwhile, but they show only weak P-S converted phases, which proved difficult to interpret. An intensive analysis of the receiver function signals and a comparison of the results with those of other receiver function studies shows that the value of the receiver function technique for studying the crust-mantle transition underneath Iceland is limited. A rapid velocity increase in the upper 8-14 km of the crust, underlain by almost constant velocities below, accounts for much of the first 1-4 s of the receiver function signals, potentially masking phases from a Moho. Therefore, 1-D velocity profiles obtained by receiver function inversion were tested intensively by forward modelling to check the robustness of the results. Receiver function analysis of 28 sites in Iceland, equipped with broad-band seismometers during the HOTSPOT project from 1996 June to 1998 July, showed that a ubiquitous prominent Moho velocity contrast does not offer a good match of the observed receiver function signals. Instead, the character of the crust-mantle transition varies from not being detectable, to gradient zones, and discrete velocity discontinuities. A tendency to reduced S velocities is observed at about 40 km depth beneath central Iceland. By comparison with other studies, I tentatively interpret this low-velocity zone as an indication of a shallow asthenosphere. © 2006 The Authors Journal compilation © 2006 RAS.