Extreme environments are unstructured and change rapidly, making human exploration in unfamiliar areas difficult. Construction robotics can help reduce risks to human safety and property in these environments by integrating digital technology and artificial intelligence. This technology has the potential to significantly improve the quality and efficiency of construction, making it a key area for future research. Extreme environments include hazardous work sites, polluted areas, and harsh natural conditions. Our review of construction robotics in these settings highlights several knowledge gaps. We focused on four main areas: mechanism design, perception, planning, and control. Our analysis reveals challenges in practical applications, such as creating adaptable mechanisms, accurately perceiving changing environments, planning for unstructured sites, and optimizing control models. Future research should explore: biomimetic designs inspired by nature, multimodal data fusion for perception, adaptive planning strategies, and hybrid control models that combine data-driven and mechanism-based approaches.