To overcome productivity issues and revolutionize the stagnating construction industry, a large amount of research efforts has been devoted to robot-assisted construction technology. The advancements in robotics including mechanical system design, tool design, digital system design, and numerical control systems design enabled engineers to create complex geometries that are infeasible for conventional construction methods. In addition, innovative robotic systems that utilize mobile platforms, multiple robots, and unmanned aerial vehicles have demonstrated significant promise in fully automating the construction process. This work will provide a perspective on the state-of-the-art applications of robotics in the revolution of construction, where a comprehensive review of the current development of the relevant software and hardware, 3D concrete printing (3DCP), robot-assisted assembly of discrete prefabricated blocks, real-time quality monitoring and feedback control systems, and typical innovative robot-assisted structural designs are conducted. Finally, the limitations of existing robot-assisted construction technology are identified, which leads to several recommendations for future research toward fully automatic construction.