Magnetic surveys for geophysical interpretation will most usefully furnish estimates of the three components of the magnetic field vector. We review methods for obtaining this information based on scalar and tensor magnetic field measurements and point out the advantages of fluxgate vector measurements. Fluxgate vector magnetometers can be powerful instruments in magnetic mapping. The main problems in using fluxgate magnetometers arise from calibration errors and drift but these can be overcome using a quick and simple method of calibration. This method also has the advantage of compensating permanent and induced magnetic fields generated by the airplane. This is illustrated by a new aeromagnetic survey flown in the Vosges area (France). Measurement accuracy is shown to be similar to that obtained with scalar magnetometers. We take advantage of this accuracy to calculate in the Fourier domain other magnetic functions from the total-field anomaly, in particular, the magnetic gradient tensor is obtained without using any superconducting quantum devices. A similar approach is used to introduce a new magnetic anomaly tensor that is the equivalent of the pseudo-gravity tensor. Maps presented in the last sections serve as an example to illustrate the various functions, the goal of the paper being to obtain magnetic vector data from the observations without first postulating the detailed nature of the sources.