This article presents a review of the current solutions for the rheological challenge of three-dimensional concrete printing (3DCP), providing a rheological definition for printability, and an overview of the current techniques for obtaining a printable concrete, placing special emphasis on understanding structural build-up and the current mixture proportions and admixtures used to improve it. A promising alternative for improving structural build-up is the use of entrained air (EA), as bubbles, whose effects are reviewed in generic yield stress fluids and then specifically in concrete. After revision of micromechanical models and experimental trials from literature on yield stress fluid bubble suspensions and concrete, EA appears to be ideal for 3DCP when generated by anionic surfactants, as it increases static yield stress and decreases plastic viscosity. Cationic surfactants, however, maintain or slightly decrease static yield stress. It is proposed that the lubricating or stiffening property of the bubbles determines their ability to deform under the shear stress generated by the surrounding fluid. The ability to deform depends on the surfactant used to entrain the bubbles and the mixture design of the concrete. Further experimental research must be carried out for the advantages of EA to be fully realized.