Robots are versatile machines that can perform complex manipulation operations. Recent advances in industrial robotics make robots useful in a wide variety of manufacturing processes. Several recent efforts have demonstrated how robots can be used in additive manufacturing (AM) processes. This paper surveys the work focused on expanding the functional capabilities of AM processes using robots. We identify the following main capabilities realized by performing AM using robots: (1) multi-directional fabrication, (2) conformal deposition, (3) assembling prefabricated components in AM, (4) supportless AM, and (5) large-scale AM. We classify the recent literature in this area in terms of mechanisms, kinematic degrees of freedom (DOF) of the system, types of AM process, and materials. Finally, we discuss the limitations of the current work and the opportunities for future research in this area.