A key advantage of Additive Manufacturing (AM) is the opportunity to design and fabricate complex structures that cannot be made via traditional means. However, this potential is significantly constrained by the use of a facet-based geometry representation (e.g., the STL and the AMF file formats); which do not contain any volumetric information and often, designing/slicing/printing complex geometries exceeds the computational power available to the designer and the AM system itself. To enable efficient design and fabrication of complex/multi-material complex structures, several algorithms are presented that represent and process solid models as a set of voxels (three-dimensional pixels). Through this, one is able to efficiently realize parts featuring complex geometries and functionally graded materials. This thesis specifically aims to explore applications in three distinct fields namely, (i) Design for AM, (ii) Design for Manufacturing (DFM) education, and (iii) Reverse engineering from imaging data wherein voxel-based representations have proven to be superior to the traditional AM digital workflow. The advantages demonstrated in this study cannot be easily achieved using traditional AM workflows, and hence this work emphasizes the need for development of new voxel based frameworks and systems to fully utilize the capabilities of AM.