The main magnetic characteristics regarding the domain structure and magnetization processes (axial, circular and Matteucci and inverse Wiedemann effects) of amorphous wires and glass-coated microwires are analysed. Magnetic bistability, spontaneously observed in samples with large enough ratio magneto-elastic anisotropy with axial easy axis to shape anisotropy, is the main source for a number of sensor applications in pulse generators, position and field sensors, encoded security tags, rotational counters, magnetostrictive delay lines, and so on. The relevant perspectives of the novel giant magneto-impedance effect recently reported and observed in non-magnetostrictive samples are also introduced.