We propose and demonstrate three-dimensional rearrangements of single atoms. In experiments performed with single Rb-87 atoms in optical microtraps actively controlled by a spatial light modulator, we demonstrate various dynamic rearrangements of up to N = 9 atoms including rotation, 2D vacancy filling, guiding, compactification, and 3D shuffling. With the capability of a phase-only Fourier mask to generate arbitrary shapes of the holographic microtraps, it was possible to place single atoms at arbitrary geometries of a few mu m size and even continuously reconfigure them by conveying each atom. For this purpose, we loaded a series of computer-generated phase masks in the full frame rate of 60 Hz of the spatial light modulator, so the animation of phase mask transformed the holographic microtraps in real time, driving each atom along the assigned trajectory. Possible applications of this method of transformation of single atoms include preparation of scalable quantum platforms for quantum computation, quantum simulation, and quantum many-body physics. (C) 2016 Optical Society of Americ