Three-dimensional (3D) inversion of magnetic data to recover a distribution of magnetic susceptibility has been successfully used for mineral exploration during the last decade. However, the unknown direction of magnetization has limited the use of this technique when significant remanence is present. We have developed a comprehensive methodology for solving this problem by examining two classes of approaches and have formulated a suite of methods of practical utility. The first class focuses on estimating total magnetization direction and then incorporating the resultant direction into an inversion algorithm that assumes a known direction. The second class focuses on direct inversion of the amplitude of the magnetic anomaly vector. Amplitude data depend weakly upon magnetization direction and are amenable to direct inversion for the magnitude of magnetization vector in 3D subsurface. Two sets of high-resolution aeromagnetic data acquired for diamond exploration in the Canadian Arctic are used to illustrate the methods’ usefulness.