Here, we present a class of small-scale soft electromagnetic robots made of curved elastomeric bilayers, driven by Lorentz forces acting on embedded printed liquid metal channels carrying alternating currents with driving voltages of several volts in a static magnetic field. Their tethered versions reach ultra-high running speeds of 70 BL/s (body lengths per second) on 3D-corrugated substrates and 35 BL/s on arbitrary planar substrates while their maximum swimming speed is 4.8 BL/s in water.