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 ${\rm Co}_{69.2}{\rm Fe}_{4.1}{\rm B}_{11.8}{\rm Si}_{13.8}{\rm C}_{1.1}$ 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.