Several researchers have worked in the field of implementing robotics technology in concrete building construction, after the first attempt in the 1980s in Japan. Various motivations such as the shrinking labor population, the aging of skilled workers, and the construction safety issues have promoted the development of such technologies. However, the future visionary on how construction robots can transform the concrete building construction sector is still not solid nor well structured. What really needs to be changed? What types of construction activities can be taken by automated robotic technologies, as opposed to manpower or skilled worker? To answer these questions, the systematic review reported in this paper seeks to evaluate and synthesize empirical findings on the use of robotic technologies in concrete building construction. A systematic search of Scopus, Web of Science, IEEE, and Engineering Village databases was conducted, and 48,200 documents were targeted. By applying the inclusion and exclusion criteria, 48,149 records were excluded, and the remaining 51 records were assessed for eligibility and included in the qualitative synthesis. The systematic review shows that researchers in the USA played a leading role on robotics in concrete building construction, followed by Germany and Switzerland. The robotics application and techniques have been largely used on-site and targeted low-rise buildings. The robotic technologies that have been popular in literature included 3D printers, and swarm robotics. Most of the papers have proposed a limited novel structural design, without introducing innovative construction material. Even though the direct and indirect construction activities related to formwork, steel reinforcement, and concreting can be replaced and thus eliminated, the horizontal RC elements still cannot be built on-site without supports. Moreover, rapid prototyping found to be the best robotic design for the purpose of building construction through utilizing manipulator robots.