The application of robotic technologies in building construction leads to great convenience and productivity improvement, and construction robots (CRs) bring enormous opportunities for the way we conduct design and construction. To get a better understanding of the trends and track the application of CRs for on‐site conditions, this paper conducts a systematic review of control models and status monitoring of CRs, which are two key aspects that determine construction accuracy and efficiency. Control accuracy and flexibility are primary needs for CRs applied in different scenes, so the control methods based on driving models are vitally important. Status monitoring on CRs contains knowledge in fault detection, intelligence maintenance, and fault‐tolerant control, and multiple objectives need to be met and optimized in the whole drive chain. Moreover, the state‐of‐the‐art is comprehensively summarized, and new insights are also provided to carry on promising researches.