We present the domain wall dynamics in amorphous glass-coated microwires. It is described by the linear dependence of the domain wall velocity on the applied magnetic field. For higher Ni content microwires, the domain wall dynamics consists of two regions: at low field, the domain wall has low mobility and a negative critical propagation field. At higher fields, the domain wall mobility increases as a result of the domain wall structure change. The domain wall dynamics in this range is described by positive critical propagation field and high domain wall mobility, which allows the domain wall to reach a very high velocity of more than 10\thinspace 000 m/s. Such a fast domain wall exceeds the sound velocity in microwires. The interaction of the domain wall with the phonons is observed when the domain wall approaches the sound velocity limit.