We overviewed the correlation between the structure, magnetic and transport properties of magnetic microwires prepared by the Taylor-Ulitovsky method involving rapid quenching from the melt and drawing of the composite (metallic core, glass coated) wire. We showed that this method can be useful for the preparation of different families of magnetic microwires: soft magnetic microwires displaying Giant magnetoimpedance (GMI) effect, semi-hard magnetic microwires, microwires with granular structure exhibiting Giant Magnetoresistance (GMR) effect and Heusler-type microwires. Magnetic and transport properties of magnetic microwires depend on the chemical composition of metallic nucleus and on the structural features (grain size, precipitating phases) of prepared microwires. In all families of crystalline microwires, their structure, magnetic and transport properties are affected by internal stresses induced by the glass coating, depending on the quenching rate. Therefore, properties of glass-coated microwires are considerably different from conventional bulk crystalline alloys.