Air-ground collaborative robots have shown great potential in the field of fire and rescue, which can quickly respond to rescue needs and improve the efficiency of task execution. Mapping and navigation, as the key foundation for air-ground collaborative robots to achieve efficient task execution, have attracted a great deal of attention. This growing interest in collaborative robot mapping and navigation is conducive to improving the intelligence of fire and rescue task execution, but there has been no comprehensive investigation of this field to highlight their strengths. In this paper, we present a systematic review of the ground-to-ground cooperative robots for fire and rescue from a new perspective of mapping and navigation. First, an air-ground collaborative robots framework for fire and rescue missions based on unmanned aerial vehicle (UAV) mapping and unmanned ground vehicle (UGV) navigation is introduced. Then, the research progress of mapping and navigation under this framework is systematically summarized, including UAV mapping, UAV/UGV co-localization, and UGV navigation, with their main achievements and limitations. Based on the needs of fire and rescue missions, the collaborative robots with different numbers of UAVs and UGVs are classified, and their practicality in fire and rescue tasks is elaborated, with a focus on the discussion of their merits and demerits. In addition, the application examples of air-ground collaborative robots in various firefighting and rescue scenarios are given. Finally, this paper emphasizes the current challenges and potential research opportunities, rounding up references for practitioners and researchers willing to engage in this vibrant area of air-ground collaborative robots.