We report on the magnetic properties and giant magnetoimpedance (GMI) effect of amorphous glass-coated Co-rich microwires in as-prepared and annealed states. The magnetic field and frequency dependences of GMI, magnetic hysteresis loops, and domain wall (DW) dynamics of Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">69.2</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4.1</sub> B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11.8</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">13.8</sub> C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.1</sub> microwires produced by the Taylor-Ulitovski technique were investigated systematically. We have shown that these properties can be tailored either by controlling magnetoelastic anisotropy of the as-prepared microwires or by controlling their magnetic anisotropy via proper annealing. While the GMI effect has been achieved in an as-prepared microwire, high DW velocity and rectangular hysteresis loops have been observed in its annealed counterpart.