Updated concrete construction robots are designed to optimize equipment operation, improve safety, enhance workspace awareness, and further ensure a proper working environment for construction workers. The importance of concrete construction robots has been constantly highlighted, as they have a profound impact on construction quality and efficiency. Autonomous vehicle driving monitoring has been widely employed in concrete construction robots; however, they lack clear relevance to the key functions in the building process. This paper aims to bridge this knowledge gap by systematically classifying and summarizing the existing concrete construction robots, analyzing their existing problems, and providing direction for their future development. The prescription criteria and selection of robots depend on the concrete construction process, which includes six common functional levels: distribution, leveling and compaction, floor finishing, surface painting, 3D printing, and surveillance. Misunderstood functions and the improper adjustment of construction robots may lead to increased cost, reduced effectiveness, and restricted application scenarios. Our review identifies current commercial and recently studied concrete construction robots to facilitate the standardization and optimization of robotic construction design. Moreover, this study may be able to guide future research and technology development efforts for autonomous robots in concrete construction.