Additive manufacturing (AM) has experienced exponential growth over the past two decades and now stands on the cusp of a transformative paradigm shift into the realm of multi-functional component manufacturing, known as multi-material AM (MMAM). While progress in MMAM has been more gradual compared to single-material AM, significant strides have been made in exploring the scientific and technological possibilities of this emerging field. Researchers have conducted feasibility studies and investigated various processes for multi-material deposition, encompassing polymeric, metallic, and bio-materials. To facilitate further advancements, this review paper addresses the pressing need for a consolidated document on MMAM that can serve as a comprehensive guide to the state of the art. Previous reviews have tended to focus on specific processes or materials, overlooking the overall picture of MMAM. Thus, this pioneering review endeavors to synthesize the collective knowledge and provide a holistic understanding of the multiplicity of materials and multiscale processes employed in MMAM. The review commences with an analysis of the implications of multiplicity, delving into its advantages, applications, challenges, and issues. Subsequently, it offers a detailed examination of MMAM with respect to processes, materials, capabilities, scales, and structural aspects. Seven standard AM processes and hybrid AM processes are thoroughly scrutinized in the context of their adaptation for MMAM, accompanied by specific examples, merits, and demerits. The scope of the review encompasses material combinations in polymers, composites, metals-ceramics, metal alloys, and biomaterials. Furthermore, it explores MMAM’s capabilities in fabricating bi-metallic structures and functionally/compositionally graded materials, providing insights into various scale and structural aspects. The review culminates by outlining future research directions in MMAM and offering an overall outlook on the vast potential of multiplicity in this field. By presenting a comprehensive and integrated perspective, this paper aims to catalyze further breakthroughs in MMAM, thus propelling the next generation of multi-functional component manufacturing to new heights by capitalizing on the unprecedented possibilities of MMAM.