We probe the current-induced magnetic switching of insulating antiferromagnet/heavy metals systems, by electrical spin Hall magnetoresistance measurements and direct imaging, identifying a reversal occurring by domain wall (DW) motion. We observe switching of more than one third of the antiferromagnetic domains by the application of current pulses. Our data reveal two different magnetic switching mechanisms leading together to an efficient switching, namely the spin-current induced effective magnetic anisotropy variation and the action of the spin torque on the DWs.