The technology of additive manufacturing, especially 3D concrete printing (3DCP), has been recently adopted in the construction industry as a viable alternative to traditional construction methods. Although the technology offers a wide variety of structural, economic, and environmental benefits, it is still restricted in use due to certain limitations that are still under research. This paper explains the fundamentals of the 3D printing process, its potential, challenges, as well as the different 3D printing systems. The recent literature is explored for recommended materials that possess the required properties for 3D printing, as well as reinforcement methods and techniques. This paper also reviews 3D printing extrusion using concrete and foam and explores the effect of both materials and extruding systems on the final product. The application of different additive construction systems with Building Information Modeling (BIM)-integrated algorithms are also discussed in this paper. It is believed that with providing a comprehensive knowledge of 3D printing for concrete construction, there is a huge potential to change the way cementitious materials are formulated and sustainability aspects are implemented, especially for complicated designs.