Nowadays, robot-based additive manufacturing (RBAM) is emerging as a potential solution to increase manufacturing flexibility. Such technology allows to change the orientation of the material deposition unit during printing, making it possible to fabricate complex parts with optimized material distribution. In this context, the representation of parts geometries and their subsequent processing become aspects of primary importance. In particular, part orientation, multiaxial deposition, slicing, and infill strategies must be properly evaluated so as to obtain satisfactory outputs and avoid printing failures. Some advanced features can be found in commercial slicing software (e.g., adaptive slicing, advanced path strategies, and nonplanar slicing), although the procedure may result excessively constrained due to the limited number of available options. Several approaches and algorithms have been proposed for each phase and their combination must be determined accurately to achieve the best results. This paper reviews the state-of-the-art works addressing the primary methods for the representation of geometries and the subsequent geometry processing for RBAM. For each category, tools and software found in the literature and commercially available are discussed. Comparison tables are then reported to assist in the selection of the most appropriate approaches. The presented review can be helpful for designers, researchers and practitioners to identify possible future directions and open issues.