Recent technological advances suggest that we are on the threshold of a new era in applied magnetic surverys, where acquisition of magnetic gradient tensor data will become routine. In the meantime, modern ultrahigh resolution conventional magnetic data can be use to calculate gradient tenor elements from TMI or TMI gradient surveys. Until the present, not a great deal of attention has been paid to processing and interpretation of gradient tensor data. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for a number of elementary, but useful, models. these include point pole, line of poles, point dipole (sphere), line of dipoles ( horizontal cylinder), thin and think dipping sheets and sloping step models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor.