The surface impedance tensor approach has been used to review the impedance response in a variety of amorphous and nanocrystallized wires. An experimental study on the torsion annealing effect on the magnetoimpedance (MI) behaviour for positive and negative magnetostriction amorphous wires of FeSiB and CoSiB compositions, respectively, has been carried out. Moreover, the influence of the onset nanocrystallization on the MI behaviour in Finemet-type alloys, with particular attention focussed on the case that the wires are annealed under applied torsional stress, is also presented. The analysis of the MI and torsion-impedance (TI) effects allows us to compare the different magnetic characteristics observed in a variety of wires. Special attention is paid to new results of the off-diagonal MI huge responses of these ferromagnetic samples, which are also a very useful source of information on the magnetic properties of the wires.