Summary Our inversion method for global conductivity structures uses a forward solver that can represent arbitrary conductivity distributions in a sphere. The inversion uses new methods of grid generation and integration on a convex hull in spherical domains and exploits the relatively high speed and modest memory requirements of the spherical basis expansion. The method reduces the forward problem to the solution of a set of stiff ordinary differential equations, which are solved by finite differences on an adaptive grid. The model is parameterized by a set of regional 1-D models, which then are interpolated into a fully 3-D spherical model using a Delaunay triangulation. The inversion proceeds in two stages: the first is a nonlinear search in which parameters are varied sequentially to minimize the cost function; the second uses a linearized inversion about the model obtained in the first stage. We have used this method to invert data at 16 frequencies from 20 geomagnetic observatories around the world. The 3-D model is generated from radial profiles (five layers) at 56 locations on the globe.