Architected materials are a unique and emerging class of materials where performance is fundamentally controlled by geometry at multiple length scales, from the nano- to the macroscale, rather than chemical composition alone. As a result, the realization of these remarkable materials is contingent upon the ability to faithfully reproduce the designed architecture. This presents fundamental challenges in fabrication due to the required three-dimensional complexity, multiple length scales, range of material constituents, possibility of multiple materials in a single architecture, and overall manufacturing throughput. Additive manufacturing (AM) processes can provide solutions to some of these challenges and are discussed in this article. Specifically, light-based and extrusion-based processes and associated materials are presented with an emphasis on recent developments, including volumetric additive manufacturing, and on-the-fly mixing of materials in extrusion-based printing systems. While remarkable advancements have been made in AM for architected materials, bringing these materials and processes to industrial realization remains a significant challenge.