For 40 years magnetic anisotropy has provided successful geological interpretations of magnetic ellipsoid orientations; in contrast the interpretation of anisotropy magnitudes is far more convoluted. This is due to complexities at various levels within rocks, including different physical magnetic responses of different minerals, grain-scale magnetic anisotropy, the anisotropy of interacting ensembles, the mineralogical constitution of rocks and the processes and mechanisms that align minerals in nature. The chief factors determining the magnetic fabrics of tectonized rocks include: mineral-physics properties, crystal symmetry, mineral-abundances, tectonic symmetry and crystal orientation-distribution, strain or stress, kinematic history and certain tectono-metamorphic processes (e.g. diffusion, crystal plasticity, dynamic recrystallization, particulate flow, neomineralization). AMS ultimately provides an integrated record of some combination of these factors. Subfabrics due to distinct processes or events may be expressed in different mineral and/or grain-size fractions, and are superposed in the conventionally observed AMS. Their discrimination may be achieved by various laboratory techniques such as magnetization and torque measurements in weak and strong applied fields, anisotropy of ARM and IRM, gyroremanence, Rayleigh magnetization, chemical leaching. However, under limited circumstances, statistical approaches such as differential analysis, tensor standardization, symmetry of confidence regions for the principal axes may partly isolate different subfabric orientations.