S U M M A R YData from recent satellite missions have vastly increased the resolution of models of the geomagnetic field, and its first and second time derivatives -secular variation (SV) and secular acceleration (SA). The spectra of both SV and SA are 'blue' at the core-mantle boundary, both well-fit by functions proportional to l(l + 1) where l is the spherical harmonic degree. The ratio of the two spectra defines a timescale for geomagnetic variations of approximately 10 yrs for all resolvable harmonic degrees. The blue spectra should prevent meaningful maps of the SV being generated; nevertheless, the coherence of the maps up to harmonic degree 13 suggests that it is possible to obtain useful insight from their examination. Low SV is confirmed under the Pacific, but also revealed under the North Atlantic and Antarctica. These features are more readily explained in terms of dynamo control through thermal core-mantle coupling than by electromagnetic screening. Comparison with maps from measurements prior to the recent satellites, using the 'Comprehensive Model', suggests that models back to at least 1970 are sufficiently good to enable direct comparison of the SV.