Novel trends in the study of magnetically soft Co-based amorphous glass-coated wires

► The most recent advances in the study of amorphous glass-coated wires with nearly zero magnetostriction are surveyed. ► Major progress in the study of their domain structure: the wide interdomain wall, which affects high frequency phenomena. ► The magnetization of the outer shell depends on wire diameter and affects the wall propagation in bistable samples. ► These novel results are important for future sensor applications of nearly zero magnetostrictive amorphous microwires.