A magnetic susceptibility tomographic device has sensitive magnetic sensors about a measurement volume and AC bias coils for providing magnetic fields within the volume. Sensing circuitry reads the sensors, and a processor executes magnetic susceptibility tomography (MST) routines from memory to divide the measurement volume into voxels, to determine differences between applied and measured field strengths of magnetic fields at each voxel and thereby determines magnetic susceptibility of each voxel, and to construct tomographic images representative of magnetic susceptibility as MST images. Embodiments with SQUID and fluxgate sensors are described. Applications to direct measurement of tissue magnetic susceptibility, and to locating and quantifying tagged magnetic nanoparticles are disclosed, including antibody-tagged nanoparticles for use in cancer diagnosis and treatments, and the retrieval of taggant identification codes from an object.