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Nearly zero magnetostrictive amorphous glass-coated microwires are very versatile due to their very good soft magnetic properties and to the appearance of sensitive application-related effects, such as the large Barkhausen and the giant magneto-impedance effects. Their specific magnetic behavior and properties originate in their unique core-shell magnetic domain structure. In this paper we address two very important aspects related to the surface magnetic structure of these materials: (i) – the necessity to include the interdomain wall that separates the inner core and the outer shell in any analysis of high frequency phenomena, and (ii) – the structure of the outer shell. Both these aspects have very important consequences as concerns the sensor applications of microwires, especially those based on the giant magneto-impedance effect.