Design for additive manufacturing (DfAM) provides a necessary framework for using novel additive manufacturing (AM) technologies for engineering innovations. Recent AM advances include shaping nickel-based superalloys for lightweight aerospace applications, reducing environmental impacts with large-scale concrete printing, and personalizing food and medical devices for improved health. Although many new capabilities are enabled by AM, design advances are necessary to ensure the technology reaches its full potential. Here, DfAM research is reviewed in the context of Fabrication, Generation, and Assessment phases that bridge the gap between AM capabilities and design innovations. Materials, processes, and constraints are considered during fabrication steps to understand AM capabilities for building systems with specified properties and functions. Design generation steps include conceptualization, configuration, and optimization to drive the creation of high-performance AM designs. Assessment steps are necessary for validating, testing, and modeling systems for future iterations and improvements. These phases provide context for discussing innovations in aerospace, automotives, construction, food, medicine, and robotics while highlighting future opportunities for design services, bio-inspired design, fabrication robots, and machine learning. Overall, DfAM has positively impacted diverse engineering applications, and further research has great potential for driving new developments in design innovation.