Complete models of highly-magnetostrictive Terfenol-D transducers must be able to characterize the magnetostriction upon knowledge of the impressed electrical energy. Fundamental characterization laws are not available at present, because the existing modeling techniques fail to simultaneously span all operating regimes: electric, magnetic, mechanical, and thermal, across the whole performance space of these transducers. This paper attempts to capture the essential aspects of these regimes and their interactions, i.e. those that the transducer designer is likely to encounter during design, analysis and modeling of magnetostrictive devices. The issues discussed here are the magnetization and stress states, thermal effects, magnetomechanical hysteresis, AC losses, system nonlinearities, and transducer dynamics. In addition, some of the more relevant modeling techniques that address these issues are presented and analyzed.