3D printing (or additive manufacturing) of concrete has been revolutionizing and remodeling the construction world. It offers digital, automated construction on Earth and beyond, but with the challenges of applicability and robustness. Leading figures from the concrete community worldwide review the state-of-the-art from properties, materials, and modeling perspectives, with case studies of practical implementation in the construction industry. It gives an overview of fresh and hardened properties of 3D printed concrete as well as a discussion on existing reinforcement strategies; it discusses advanced 3D printable materials and mixture proportioning; it outlines the pros and cons, including the problems of constructability; and it describes innovative modelling technologies.