Metros (heavy rail transit systems) are integral parts of urban transportation systems. Failures in their operations can have serious impacts on urban mobility, and measuring their robustness is therefore critical. Moreover, as physical networks, metros can be viewed as network topological entities, and as such they possess measurable network properties. In this paper, by using network science and graph theoretical concepts, we investigate both theoretical and experimental robustness metrics (i.e., the robustness indicator, the effective graph conductance, and the critical thresholds) and their performance in quantifying the robustness of metro networks under random failures or targeted attacks. We find that the theoretical metrics quantify different aspects of the robustness of metro networks. In particular, the robustness indicator captures the number of alternative paths and the effective graph conductance focuses on the length of each path. Moreover, the high positive correlation between the theoretical metrics and experimental metrics and the negative correlation within the theoretical metrics provide significant insights for planners to design more robust system while accommodating for transit specificities (e.g., alternative paths, fast transferring).