We demonstrate the trapping and manipulation of single neutral atoms in reconfigurable arrays of optical tweezers. Our approach offers unparalleled speed by using a Texas instruments digital micro-mirror device as a holographic amplitude modulator with a frame rate of 20 000 per second. We show the trapping of static arrays of up to 20 atoms, as well as transport of individually selected atoms over a distance of 25 μm with laser cooling and 4 μm without. We discuss the limitations of the technique and the scope for technical improvements.