The goal of electromagnetic (EM) inversion for mineral exploration has long been to recover 3D models with high conductivity contrasts, heterogeneous hosts and arbitrary geometric complexity such as topography and unconforming interfaces, for any type of EM system. In the work presented here, this is achieved using a 3D full-domain edge-element finite-element method which enables the accurate modelling of arbitrarily complex 3D models with conductivity contrasts up to 106:1. Inversion is based on the iterative Gauss-Newton method, which is solved using either SVD or model norm regularization. The accurate and efficient computation of the sensitivities is critical to the practicality of the software. We introduce the domain differentiation method for this purpose, and compare its results to those obtained using the adjoint operator method. Mineral exploration case studies are presented for the inversion of ground and airborne EM data. The integration of these results for interpreting 3D geological structure is also discussed. Technical Area: Minerals – Inversion