It is thought that dislocations cannot surpass the sound barrier at the shear wave velocity because the energy spent in radiation has a singularity there. Atomistic simulations show that dislocations can move faster than the speed of sound if they are created as supersonic dislocations at a strong stress concentration and are subjected to high shear stresses. This behavior is important for the understanding of low-temperature deformation processes such as mechanical twinning and may be relevant for the dynamics of tectonic faults. The motion of the dislocations at a speed of root 2 times the shear wave velocity can be understood from a Linear elastic analysis, but many of the peculiarities of the supersonic dislocations are dominated by nonlinear effects that require a realistic atomistic description.