A microscopic calculation is presented for the spin-transfer torques (STT) and damping torques in metallic antiferromagnets (AF). It is found that the sign of the STT is opposite to that in ferromagnets because of the AF transport character, and the current-to-STT conversion factor is enhanced near the AF gap edge. The dissipative torque parameter $\beta_n$ and the damping parameter $\alpha_n$ for the N\'eel vector arise from spin relaxation of electrons. Physical consequences are demonstrated for the AF domain wall motion using collective coordinates, and some similarities to the ferromagnetic case are pointed out such as intrinsic pinning and the specialty of $\alpha_n = \beta_n$. A recent experiment on a ferrimagnetic GdFeCo near its angular-momentum compensation temperature is discussed.
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