Recent advances in manufacturing and material science enable the fabrication of complex digital geometric models that are difficult or impossible to produce by using conventional manufacturing technologies. The unprecedented manufacturing flexibility offers opportunities and challenges for computer-aided design of such digital models. Even for the most experienced designers, their intuition might be limited when manually exploring such unprecedented large design space. To empower designers, computer algorithms are being developed to generate desired designs under given design objectives and constraints. Such an algorithm-driven design process is now known as generative design. Example approaches range from shape and topology optimization to shape grammar based design, and to machine learning based designs, among others. The flexibilities in generative design and additive manufacturing are increasingly being combined to produce disruptive high-performance functional structures and digital materials with applications in aerospace, automotive, medical implants, soft robots, customized consumer products, and beyond. This vibrant research area is receiving growing attention in multiple disciplines, such as geometric modeling, graphics, numerical optimization, and computational mechanics.